The quantum measurement problem.
Leggett, A J
2005-02-11
Despite the spectacular success of quantum mechanics (QM) over the last 80 years in explaining phenomena observed at the atomic and subatomic level, the conceptual status of the theory is still a topic of lively controversy. Most of the discussion centers around two famous paradoxes (or, as some would have it, pseudoparadoxes) associated, respectively, with the names of Einstein, Podolsky, and Rosen (EPR) and with Schrodinger's cat. In this Viewpoint, I will concentrate on the paradox of Schrodinger's cat or, as it is often known (to my mind somewhat misleadingly), the quantum measurement paradox.
Measure problem in slow roll inflation and loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh
2011-01-01
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
The measurement problem in quantum mechanics: A phenomenological investigation
Hunter, Joel Brooks
2008-10-01
This dissertation is a phenomenological investigation of the measurement problem in quantum mechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality
On the problem of measurement in quantum mechanics
International Nuclear Information System (INIS)
He Zuoxiu
1993-01-01
Some new developments in the theory of measurement in quantum mechanics are presented. The theory of measurement given by Von Neumann is shown to be incorrect, since the process of measurement is one of increasing entropy and cannot be derived within the scope of Schroedinger's equation. The new theory developed by Daneri, Loinger and Prosperi can avoid the difficulties previously encountered and, furthermore, can explain the EPR paradox
Quantum Statistics and Entanglement Problems
Trainor, L. E. H.; Lumsden, Charles J.
2002-01-01
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize here the remarkable role of quantum statistics in describing the entanglement problem correctly and discuss the relationship to issues arising from current discussions of intelligent observers in entangled, decohering quantum worlds.
Busch, Paul; Pellonpää, Juha-Pekka; Ylinen, Kari
2016-01-01
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4....
What quantum measurements measure
Griffiths, Robert B.
2017-09-01
A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent histories. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. Applications include Einstein's hemisphere and Wheeler's delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if [A ,B ]=[A ,C ]=0 ,[B ,C ]≠0 , the outcome of an A measurement does not depend on whether it is measured with B or with C . An application to Bohm's model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox.
Measurement in quantum physics
International Nuclear Information System (INIS)
Danos, M.; Kieu, T.D.; Columbia Univ., New York, NY
1997-01-01
The conceptual problems in quantum mechanics - including the collapse of the wave functions, the particle-wave duality, the meaning of measurement-arise from the need to ascribe particle character to the wave function, which describes only the wave aspects. It is demonstrated that all these problems can be resolved when working instead with quantum fields, which have both wave and particle character. The predictions of quantum physics, including Bell's inequalities, remain unchanged from the standard treatments of quantum mechanics. 16 refs
Johnson, David T.
Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Decoherence and quantum measurements
Namiki, Mikio; Pascazio, Saverio
1997-01-01
The quantum measurement problem is one of the most fascinating and challenging topics in physics both theoretically and experimentally. It involves deep questions and the use of very sophisticated and elegant techniques. After analyzing the fundamental principles of quantum mechanics and of the Copenhagen interpretation, this book reviews the most important approaches to the measurement problem and rigorously reformulates the "collapse of the wave function" by measurement, as a dephasing process quantitatively characterized by an order parameter (called the decoherence parameter), according to
International Nuclear Information System (INIS)
Kumar, N.
1984-07-01
Quantum first passage problem (QUIPP) is formulated and solved in terms of a constrained Feynman path integral. The related paradox of blocking of unitary evolution by continuous observation on the system implicit in QUIPP is briefly discussed. (author)
International Nuclear Information System (INIS)
Usera, J.I.
1996-01-01
An approach based on bits and pieces of standard wisdom plus and operational quantum mechanical identity deduced by the author is presented here in order to convey arguments concerning the quantum theory of measurement and which betray a flavor against completive claims for quantum mechanics. Special emphasis is put on the phenomenon of decoherence. This phenomenon (which is experimentally verifiable) finds natural room within the formalism while the wave function collapse (which is not) is precluded. (Author)
A criticism to the fundamental principles of physics: The problem of the quantum measurement (I)
International Nuclear Information System (INIS)
Mormontoy Cardenas, Oscar; Marquez Jacome, Mateo
2008-01-01
The wave packet model collapse debt to extremely fast fluctuations of quantum field leads to interpreting the phase speed of the harmonic waves that compose the packet, as the speed of time flux. If it consider that harmonics waves keep different phases, the waves packet scattered almost instantly and, as consequence of that, allows the possibility of the quantum system energy it is measure with exactitude absolute in given time. These results induce to think that the time would being a superforce which would determine finally the events of universe and being responsible of the intrinsic pulsations observable in the physics systems. (author)
Quantum measurement in quantum optics
International Nuclear Information System (INIS)
Kimble, H.J.
1993-01-01
Recent progress in the generation and application of manifestly quantum or nonclassical states of the electromagnetic field is reviewed with emphasis on the research of the Quantum Optics Group at Caltech. In particular, the possibilities for spectroscopy with non-classical light are discussed both in terms of improved quantitative measurement capabilities and for the fundamental alteration of atomic radiative processes. Quantum correlations for spatially extended systems are investigated in a variety of experiments which utilize nondegenerate parametric down conversion. Finally, the prospects for measurement of the position of a free mass with precision beyond the standard quantum limit are briefly considered. (author). 38 refs., 1 fig
International Nuclear Information System (INIS)
Amsterdamski, P.
1986-01-01
The standard cosmological model is reviewed and shown not to be self-sufficient in that it requires initial conditions most likely to be supplied by quantum cosmology. The possible approaches to the issue of initial conditions for cosmology are then discussed. In this thesis, the author considers three separate problems related to this issue. First, the possibility of inflation is investigated in detail by analyzing the evolution of metric perturbations and fluctuations in the expectation value of a scalar field prior to a phase transition; finite temperature effects are also included. Since the inhomogeneities were damped well before the onset of a phase transition. It is concluded that an inflation was possible. Next, the effective action of neutrino and photon fields is calculated for homogeneous spacetimes with small anisotropy; it is shown that quantum corrections to the action due to these fields influence the evolution of an early Universe in the Same way as do the analogous correction terms arising from a conformally invariant scalar which has been previously studied. Finally, the question of an early anisotropy is also discussed in a framework of Hartle-Hawking wave function of the Universe. A wave function of a Bianchi IX type Universe is calculated in a semiclassical approximation
Quantum measurement and dynamical maps
International Nuclear Information System (INIS)
Sudarshan, E.C.G.
1985-01-01
The problem of measurement in a quantum system involves the interaction of a classical system with only a small number of degrees of freedom ('measuring apparatus') coupled to the quantum system which is being subjected to measurement. It has been the practice to think of the measuring apparatus as a quantum system with a very large number of degrees of freedom treated in the classical limit. It is, however, possible to formulate the problem in such a manner that the measuring apparatus is a classical system with a finite number of degrees of freedom; this involves the perception of the classical system as the projection of a quantum system. The use of dynamical maps, which are discussed in this paper, is shown to be of benefit in tackling this problem. (UK)
The quantum theory of measurement
Busch, Paul; Mittelstaedt, Peter
1996-01-01
The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables and unsharp pointers.
de Raedt, Hans; von der Linden, W.; Binder, K
1995-01-01
In this chapter we review methods currently used to perform Monte Carlo calculations for quantum lattice models. A detailed exposition is given of the formalism underlying the construction of the simulation algorithms. We discuss the fundamental and technical difficulties that are encountered and
Substantiating problems of quantum mechanics
International Nuclear Information System (INIS)
Gottlieb, J.
1978-05-01
Some basic problems, related to the spaces and the operators necessary to describe quantum-mechanical phenomena, are entered upon from a new axiomatic standpoint. Some generalizations are operated, required by convergence criteria, concerning the Fourier transform, the Fourier product and the equation of eigen-values. Physical arguments are brought to support such generalizations and an analysis in view of organizing the structure of the proposed spaces is undertaken. (author)
Quantum complexity of graph and algebraic problems
International Nuclear Information System (INIS)
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Quantum complexity of graph and algebraic problems
Energy Technology Data Exchange (ETDEWEB)
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Weak Measurement and Quantum Correlation
Indian Academy of Sciences (India)
Arun Kumar Pati
Entanglement: Two quantum systems can be in a strongly correlated state even if .... These are resources which can be used to design quantum computer, quantum ...... Weak measurements have found numerous applications starting from the ...
Quantum learning algorithms for quantum measurements
Energy Technology Data Exchange (ETDEWEB)
Bisio, Alessandro, E-mail: alessandro.bisio@unipv.it [QUIT Group, Dipartimento di Fisica ' A. Volta' and INFN, via Bassi 6, 27100 Pavia (Italy); D' Ariano, Giacomo Mauro, E-mail: dariano@unipv.it [QUIT Group, Dipartimento di Fisica ' A. Volta' and INFN, via Bassi 6, 27100 Pavia (Italy); Perinotti, Paolo, E-mail: paolo.perinotti@unipv.it [QUIT Group, Dipartimento di Fisica ' A. Volta' and INFN, via Bassi 6, 27100 Pavia (Italy); Sedlak, Michal, E-mail: michal.sedlak@unipv.it [QUIT Group, Dipartimento di Fisica ' A. Volta' and INFN, via Bassi 6, 27100 Pavia (Italy); Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, 845 11 Bratislava (Slovakia)
2011-09-12
We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information. -- Highlights: → Optimal learning algorithm for von Neumann measurements. → From 2 copies to 1 copy: the optimal strategy is parallel. → From 3 copies to 1 copy: the optimal strategy must be non-parallel.
Quantum learning algorithms for quantum measurements
International Nuclear Information System (INIS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Sedlak, Michal
2011-01-01
We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information. -- Highlights: → Optimal learning algorithm for von Neumann measurements. → From 2 copies to 1 copy: the optimal strategy is parallel. → From 3 copies to 1 copy: the optimal strategy must be non-parallel.
Quantum discord with weak measurements
International Nuclear Information System (INIS)
Singh, Uttam; Pati, Arun Kumar
2014-01-01
Weak measurements cause small change to quantum states, thereby opening up the possibility of new ways of manipulating and controlling quantum systems. We ask, can weak measurements reveal more quantum correlation in a composite quantum state? We prove that the weak measurement induced quantum discord, called as the “super quantum discord”, is always larger than the quantum discord captured by the strong measurement. Moreover, we prove the monotonicity of the super quantum discord as a function of the measurement strength and in the limit of strong projective measurement the super quantum discord becomes the normal quantum discord. We find that unlike the normal discord, for pure entangled states, the super quantum discord can exceed the quantum entanglement. Our results provide new insights on the nature of quantum correlation and suggest that the notion of quantum correlation is not only observer dependent but also depends on how weakly one perturbs the composite system. We illustrate the key results for pure as well as mixed entangled states. -- Highlights: •Introduced the role of weak measurements in quantifying quantum correlation. •We have introduced the notion of the super quantum discord (SQD). •For pure entangled state, we show that the SQD exceeds the entanglement entropy. •This shows that quantum correlation depends not only on observer but also on measurement strength
Quantum measure and integration theory
International Nuclear Information System (INIS)
Gudder, Stan
2009-01-01
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum integral's form for simple functions is characterized and it is shown that the quantum integral generalizes the Lebesgue integral. A bounded, monotone convergence theorem for quantum integrals is obtained and it is shown that a Radon-Nikodym-type theorem does not hold for quantum measures. As an example, a quantum-Lebesgue integral on the real line is considered.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
International Nuclear Information System (INIS)
Clarke, M L
2014-01-01
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism). (paper)
Problems and solutions in quantum physics
Ficek, Zbigniew
2016-01-01
This book contains tutorial problems with solutions for the textbook Quantum Physics for Beginners. The reader studying the abstract field of quantum physics needs to solve plenty of practical, especially quantitative, problems. This book places emphasis on basic problems of quantum physics together with some instructive, simulating, and useful applications. A considerable range of complexity is presented by these problems, and not too many of them can be solved using formulas alone.
Quantum gravity and quantum nondemolition measurements
International Nuclear Information System (INIS)
Borzeszkowski, H.H. von; Treder, H.J.
1984-01-01
It is shown that in Quantum Gravity, and more general: in Grand Unified Theory incorporating General Relativity on a basic level, there arise necessarily absolute limitations on measurement which one cannot evade by any 'quantum nondemolition measurements'. This fact is demonstrated not to oppose the existence of certain approximations to the full theory where these limitations do not arise. (author)
Exploiting Quantum Resonance to Solve Combinatorial Problems
Zak, Michail; Fijany, Amir
2006-01-01
Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.
Quantum ergodicity and a quantum measure algebra
International Nuclear Information System (INIS)
Stechel, E.B.
1985-01-01
A quantum ergodic theory for finite systems (such as isolated molecules) is developed by introducing the concept of a quantum measure algebra. The basic concept in classical ergodic theory is that of a measure space. A measure space is a set M, together with a specified sigma algebra of subsets in M and a measure defined on that algebra. A sigma algebra is closed under the formation of intersections and symmetric differences. A measure is a nonnegative and countably additive set function. For this to be further classified as a dynamical system, a measurable transformation is introduced. A measurable transformation is a mapping from a measure space into a measure space, such that the inverse image of every measurable set is measurable. In conservative dynamical systems, a measurable transformation is measure preserving, which is to say that the inverse image of every measurable set has the same measure as the original set. Once the measure space and the measurable transformation are defined, ergodic theory can be investigated on three levels: describable as analytic, geometric and algebraic. The analytic level studies linear operators induced by a transformation. The geometric level is concerned directly with transformations on a measure space and the algebraic treatments substitute a measure algebra for the measure space and basically equate sets that differ only by sets of measure zero. It is this latter approach that is most directly paralleled here. A measure algebra for a quantum dynamical system is defined within which stochastic concepts in quantum mechanics can be investigated. The quantum measure algebra differs from a normal measure algebra only in that multiplication is noncommutative and addition is nonassociative. Nonetheless, the quantum measure algebra preserves the essence of a normal measure algebra
Quantum cryptography as a retrodiction problem.
Werner, A H; Franz, T; Werner, R F
2009-11-27
We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission-error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.
Experimental realization of the quantum box problem
International Nuclear Information System (INIS)
Resch, K.J.; Lundeen, J.S.; Steinberg, A.M.
2004-01-01
The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but nonorthogonal) superposition. It was predicted that appropriate 'weak' measurements of particle position in the interval between preparation and post-selection would find the particle in two different places, each with certainty. We verify these predictions in an optical experiment and address the issues of locality and of negative probability
Approach to measurement to quantum mechanics
International Nuclear Information System (INIS)
Sudarshan, E.C.G.; Sherry, T.N.; Gautam, S.R.
1977-10-01
An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a larger quantum mechanical structure, making use of superselection rules. Projection back to the classical system is possible. The apparatus and system are now coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Finally, projection back to the classical formulation is accomplished. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treat) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined
Classical randomness in quantum measurements
International Nuclear Information System (INIS)
D'Ariano, Giacomo Mauro; Presti, Paoloplacido Lo; Perinotti, Paolo
2005-01-01
Similarly to quantum states, also quantum measurements can be 'mixed', corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies give optimal apparatuses that are indecomposable. Mathematically the problem is posed describing each measuring apparatus by a positive operator-valued measure (POVM), which gives the statistics of the outcomes for any input state. The POVMs form a convex set, and in this language the indecomposable apparatuses are represented by extremal points-the analogous of 'pure states' in the convex set of states. Differently from the case of states, however, indecomposable POVMs are not necessarily rank-one, e.g. von Neumann measurements. In this paper we give a complete classification of indecomposable apparatuses (for discrete spectrum), by providing different necessary and sufficient conditions for extremality of POVMs, along with a simple general algorithm for the decomposition of a POVM into extremals. As an interesting application, 'informationally complete' measurements are analysed in this respect. The convex set of POVMs is fully characterized by determining its border in terms of simple algebraic properties of the corresponding POVMs
Adiabatic quantum search algorithm for structured problems
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size
Quantum Computing's Classical Problem, Classical Computing's Quantum Problem
Van Meter, Rodney
2013-01-01
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classica...
Quantum measurement and algebraic quantum field theories
International Nuclear Information System (INIS)
DeFacio, B.
1976-01-01
It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any ideas of ''a reading error'' or ''a measured range.'' Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal state for systems with an infinite number of degrees of freedom, including questions on open and closed algebraic theories
Quantum behaviour of measuring apparatus
International Nuclear Information System (INIS)
Amri, T.
2011-05-01
This thesis explores the quantum behavior of measurement apparatus with illustrations in quantum optics. This is the first study of quantum properties of measurements performed by any kind of devices. We show that the quantum properties of a measurement, such as its projective or non-classical character, are revealed only by the quantum states of an unusual approach of quantum physics: the retrodictive approach. This approach involves retro-predictions about state preparations leading to a given measurement result, contrary to the predictive approach with which we usually make predictions about the results of an experiment. By clarifying the mathematical foundations of the retrodictive approach, we propose a general procedure for reconstructing the quantum states of this approach: the retrodicted states. We have realized these reconstructions for single-photon detectors, widely used in quantum cryptography for instance. This is the first tomography of quantum states totally based on the retrodictive approach and preparation choices, contrary to usual reconstructions based on measurement results. These tomographies enabled us to study experimentally the noise influence on the quantum properties of measurements performed by these detectors, in particular their transition from a strongly quantum behavior into a more classical behavior. Finally, we propose a detector of Schroedinger's Cat states of light, which are superpositions of incompatible quasi-classical states of light. In a modern version of a thought experiment proposed by Eugene Wigner in 1961, such a device could allow the Wigner's Friend to detect a Schroedinger's Cat, contrary to human eyes for which we specify some quantum properties. We generalize the use of such a non-classical detector to an estimation protocol, totally based on the retrodictive approach and preparation choices. Such a procedure could enable optimal estimations, by reaching the quantum Cramer-Rao bound, which is a very topical issue
Problems in Quantum Mechanics with Solutions
d'Emilio, Emilio
2011-01-01
242 solved problems of several degrees of difficulty in nonrelativistic Quantum Mechanics, ranging from the themes of the crisis of classical physics, through the achievements in the framework of modern atomic physics, down to the still alive, more intriguing aspects connected e.g. with the EPR paradox, the Aharonov--Bohm effect, quantum teleportation.
Physics: Quantum problems solved through games
Maniscalco, Sabrina
2016-04-01
Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210
Quantum nondemolition measurements for quantum information
International Nuclear Information System (INIS)
Ralph, T. C.; O'Brien, J. L.; Bartlett, S. D.; Pryde, G. J.; Wiseman, H. M.
2006-01-01
We discuss the characterization and properties of quantum nondemolition (QND) measurements on qubit systems. We introduce figures of merit which can be applied to systems of any Hilbert space dimension, thus providing universal criteria for characterizing QND measurements. The controlled-NOT gate and an optical implementation are examined as examples of QND devices for qubits. We also consider the QND measurement of weak values
Quantum resonance for simulating combinatorial problems
International Nuclear Information System (INIS)
Zak, Michail; Fijany, Amir
2005-01-01
Quantum computing by simulations is based upon similarity between mathematical formalism of a quantum phenomenon and phenomena to be analyzed. In this Letter, the mathematical formalism of quantum resonance combined with tensor product decomposability of unitary evolutions is mapped onto a class of NP-complete combinatorial problems. It has been demonstrated that nature has polynomial resources for solving NP-complete problems and that will help to develop a new strategy for artificial intelligence, as well as to re-evaluate the role of natural selection in biological evolution
Towards quantum gravity via quantum field theory. Problems and perspectives
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2016-07-01
General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.
Optimization problem in quantum cryptography
International Nuclear Information System (INIS)
Brandt, Howard E
2003-01-01
A complete optimization was recently performed, yielding the maximum information gain by a general unitary entangling probe in the four-state protocol of quantum cryptography. A larger set of optimum probe parameters was found than was known previously from an incomplete optimization. In the present work, a detailed comparison is made between the complete and incomplete optimizations. Also, a new set of optimum probe parameters is identified for the four-state protocol
Some mass measurement problems
International Nuclear Information System (INIS)
Merritt, J.S.
1976-01-01
Concerning the problem of determining the thickness of a target, an uncomplicated approach is to measure its mass and area and take the quotient. This paper examines the mass measurement aspect of such an approach. (author)
On the quantum inverse scattering problem
International Nuclear Information System (INIS)
Maillet, J.M.; Terras, V.
2000-01-01
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains
The reality problem in quantum mechanics
International Nuclear Information System (INIS)
Flamm, D.
1988-01-01
A series of 12 lectures on quantum mechanics and its inter-pretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradoxon; Bell's inequations; interpretations of quantum theory; the role of the observer and the wave function of the world. 40 refs., 11 figs. (qui)
Universality of measurements on quantum markets
Pakuła, Ireneusz; Piotrowski, Edward W.; Sładkowski, Jan
2007-11-01
Two of the authors have recently discussed financial markets operated by quantum computers-quantum market games. These “new markets” cannot by themselves create opportunity of making extraordinary profits or multiplying goods, but they may cause the dynamism of transaction which would result in more effective markets and capital flow into hands of the most efficient traders. Here we focus upon the problem of universality of measurement in quantum market games offering a possible method of implementation if the necessary technologies would be available. It can be also used to analyse material commitments that elude description in orthodox game-theoretic terms.
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Complexity of Quantum Impurity Problems
Bravyi, Sergey; Gosset, David
2017-12-01
We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity. The full system consists of n fermionic modes and has a Hamiltonian {H=H_0+H_{imp}}, where H 0 is quadratic in creation-annihilation operators and H imp is an arbitrary Hamiltonian acting on a subset of O(1) modes. We show that the ground energy of H can be approximated with an additive error {2^{-b}} in time {n^3 \\exp{[O(b^3)]}}. Our algorithm also finds a low energy state that achieves this approximation. The low energy state is represented as a superposition of {\\exp{[O(b^3)]}} fermionic Gaussian states. To arrive at this result we prove several theorems concerning exact ground states of impurity models. In particular, we show that eigenvalues of the ground state covariance matrix decay exponentially with the exponent depending very mildly on the spectral gap of H 0. A key ingredient of our proof is Zolotarev's rational approximation to the {√{x}} function. We anticipate that our algorithms may be used in hybrid quantum-classical simulations of strongly correlated materials based on dynamical mean field theory. We implemented a simplified practical version of our algorithm and benchmarked it using the single impurity Anderson model.
Theoretical physics 3. Quantum mechanics 1 with problems in MAPLE
International Nuclear Information System (INIS)
Reineker, P.; Schulz, M.; Schulz, B.M.
2007-01-01
The following topics are dealt with: Historically heuristic introduction to quantum mechanics, the Schroedinger equation, foundations of quantum mechanics, the linear harmonic oscillator, quantum-mechanical motion in the central field, approximation methods for the solution of quantum mechanical problems, motion of particles in the electromagnetic field, spin and magnetic moment of the electron, many-particle systems, conceptional problems of quantum mechanics
Quantum mechanics and precision measurements
International Nuclear Information System (INIS)
Ramsey, N.F.
1995-01-01
The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. Although the Heisenberg Uncertainty Principle often limits measurement accuracies, in many cases the validity of quantum mechanics makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: 1) Existence of discrete quantum states of energy. 2) Energy conservation in transitions between two states. 3) Electromagnetic radiation of frequency v is quantized with energy hv per quantum. 4) The identity principle. 5) The Heisenberg Uncertainty Principle. 6) Addition of probability amplitudes (not probabilities). 7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its effect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems. These effects are discussed and illustrated
Inverse problems in classical and quantum physics
International Nuclear Information System (INIS)
Almasy, A.A.
2007-01-01
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
Inverse problems in classical and quantum physics
Energy Technology Data Exchange (ETDEWEB)
Almasy, A.A.
2007-06-29
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
The brachistochrone problem in open quantum systems
International Nuclear Information System (INIS)
Rotter, Ingrid
2007-01-01
Recently, the quantum brachistochrone problem has been discussed in the literature by using non-Hermitian Hamilton operators of different types. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al for the transmission through microwave cavities of different shapes are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of the standard quantum mechanics with the Hermitian Hamilton operator and consideration of S matrix poles
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Cloning of a quantum measurement
International Nuclear Information System (INIS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Sedlak, Michal
2011-01-01
We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1→2 learning of the measurement, otherwise the task is called 1→2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension d of the Hilbert space. For 1→2 cloning we also propose a simple quantum network that achieves the optimal fidelity. The optimal fidelity for 1→2 learning just slightly outperforms the estimate and prepare strategy in which one first estimates the unknown measurement and depending on the result suitably prepares the duplicate.
Cloning of a quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Bisio, Alessandro; D' Ariano, Giacomo Mauro; Perinotti, Paolo; Sedlak, Michal [QUIT Group, Dipartimento di Fisica ' ' A. Volta' ' and INFN, via Bassi 6, I-27100 Pavia (Italy); QUIT Group, Dipartimento di Fisica ' ' A. Volta' ' via Bassi 6, I-27100 Pavia (Italy) and Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 9, SK-845 11 Bratislava (Slovakia)
2011-10-15
We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1{yields}2 learning of the measurement, otherwise the task is called 1{yields}2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension d of the Hilbert space. For 1{yields}2 cloning we also propose a simple quantum network that achieves the optimal fidelity. The optimal fidelity for 1{yields}2 learning just slightly outperforms the estimate and prepare strategy in which one first estimates the unknown measurement and depending on the result suitably prepares the duplicate.
Quantum Inequalities and Sequential Measurements
International Nuclear Information System (INIS)
Candelpergher, B.; Grandouz, T.; Rubinx, J.L.
2011-01-01
In this article, the peculiar context of sequential measurements is chosen in order to analyze the quantum specificity in the two most famous examples of Heisenberg and Bell inequalities: Results are found at some interesting variance with customary textbook materials, where the context of initial state re-initialization is described. A key-point of the analysis is the possibility of defining Joint Probability Distributions for sequential random variables associated to quantum operators. Within the sequential context, it is shown that Joint Probability Distributions can be defined in situations where not all of the quantum operators (corresponding to random variables) do commute two by two. (authors)
Quantum game application to spectrum scarcity problems
Zabaleta, O. G.; Barrangú, J. P.; Arizmendi, C. M.
2017-01-01
Recent spectrum-sharing research has produced a strategy to address spectrum scarcity problems. This novel idea, named cognitive radio, considers that secondary users can opportunistically exploit spectrum holes left temporarily unused by primary users. This presents a competitive scenario among cognitive users, making it suitable for game theory treatment. In this work, we show that the spectrum-sharing benefits of cognitive radio can be increased by designing a medium access control based on quantum game theory. In this context, we propose a model to manage spectrum fairly and effectively, based on a multiple-users multiple-choice quantum minority game. By taking advantage of quantum entanglement and quantum interference, it is possible to reduce the probability of collision problems commonly associated with classic algorithms. Collision avoidance is an essential property for classic and quantum communications systems. In our model, two different scenarios are considered, to meet the requirements of different user strategies. The first considers sensor networks where the rational use of energy is a cornerstone; the second focuses on installations where the quality of service of the entire network is a priority.
Contiguity and quantum theory of measurement
Energy Technology Data Exchange (ETDEWEB)
Green, H.S. [Adelaide Univ., SA (Australia). Dept. of Mathematical Physics]|[Adelaide Univ., SA (Australia). Dept. of Physics
1995-12-31
This paper presents a comprehensive treatment of the problem of measurement in microscopic physics, consistent with the indeterministic Copenhagen interpretation of quantum mechanics and information theory. It is pointed out that there are serious difficulties in reconciling the deterministic interpretations of quantum mechanics, based on the concepts of a universal wave function or hidden variables, with the principle of contiguity. Quantum mechanics is reformulated entirely in terms of observables, represented by matrices, including the statistical matrix, and the utility of information theory is illustrated by a discussion of the EPR paradox. The principle of contiguity is satisfied by all conserved quantities. A theory of the operation of macroscopic measuring devices is given in the interaction representation, and the attenuation of the indeterminacy of a microscopic observable in the process of measurement is related to observable changes of entropy. 28 refs.
Contiguity and quantum theory of measurement
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1995-01-01
This paper presents a comprehensive treatment of the problem of measurement in microscopic physics, consistent with the indeterministic Copenhagen interpretation of quantum mechanics and information theory. It is pointed out that there are serious difficulties in reconciling the deterministic interpretations of quantum mechanics, based on the concepts of a universal wave function or hidden variables, with the principle of contiguity. Quantum mechanics is reformulated entirely in terms of observables, represented by matrices, including the statistical matrix, and the utility of information theory is illustrated by a discussion of the EPR paradox. The principle of contiguity is satisfied by all conserved quantities. A theory of the operation of macroscopic measuring devices is given in the interaction representation, and the attenuation of the indeterminacy of a microscopic observable in the process of measurement is related to observable changes of entropy. 28 refs
Measurement theory in quantum mechanics
International Nuclear Information System (INIS)
Klein, G.
1980-01-01
It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in a natural way in the quantum mechanics theory. There are no longer fundamental differences between macroscopic and microscopic objects, between classical and quantum objects, between observer and object. Thus, discrepancies and paradoxes have disappeared from the conventional quantum mechanics theory. One consequence of the cumulative memory of the particles is that the sum of negentropy plus information is a constant. Using this theory it is also possible to explain the 'paranormal' phenomena and what is their difference from the 'normal' ones [fr
Problems in quantum mechanics with solutions
d'Emilio, Emilio
2017-01-01
This second edition of an extremely well-received book presents more than 250 nonrelativistic quantum mechanics problems of varying difficulty with the aim of providing students didactic material of proven value, allowing them to test their comprehension and mastery of each subject. The coverage is extremely broad, from themes related to the crisis of classical physics through achievements within the framework of modern atomic physics to lively debated, intriguing aspects relating to, for example, the EPR paradox, the Aharonov-Bohm effect, and quantum teleportation. Compared with the first edition, a variety of improvements have been made and additional topics of interest included, especially focusing on elementary potential scattering. The problems themselves range from standard and straightforward ones to those that are complex but can be considered essential because they address questions of outstanding importance or aspects typically overlooked in primers. The book offers students both an excellent tool f...
Destructive quantum interference in spin tunneling problems
von Delft, Jan; Henley, Christopher L.
1992-01-01
In some spin tunneling problems, there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to destructive interference between the different paths, so that the total tunneling amplitude is zero. In the study of tunneling between different ground state configurations of the Kagom\\'{e}-lattice quantum Heisenberg antiferromagnet, this occurs when the spi...
Some basic problems of quantum electrodynamics
International Nuclear Information System (INIS)
Steinmann, O.
1981-01-01
QED (= quantum electrodynamics) is often said to be one of the most successful theories, if not 'the' most successful one, that we possess in physics. That it is a theory is, however, not yet established beyond possible doubt. In this talk I report on the present state of this problem. The question is whether the computational rules of QED, which stand up so well to all practical tests, can be founded logically in a consistent, exactly formulizable, theory. (orig./HSI)
Solving satisfiability problems by the ground-state quantum computer
International Nuclear Information System (INIS)
Mao Wenjin
2005-01-01
A quantum algorithm is proposed to solve the satisfiability (SAT) problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit exact cover problem. The time cost of this algorithm on the general SAT problems is discussed
Quantum market games: implementing tactics via measurements
International Nuclear Information System (INIS)
Pakula, I; Piotrowski, E W; Sladkowski, J
2006-01-01
A major development in applying quantum mechanical formalism to various fields has been made during the last few years. Quantum counterparts of Game Theory, Economy, as well as diverse approaches to Quantum Information Theory have been found and currently are being explored. Using connections between Quantum Game Theory and Quantum Computations, an application of the universality of a measurement based computation in Quantum Market Theory is presented
Quantum particle swarm approaches applied to combinatorial problems
Energy Technology Data Exchange (ETDEWEB)
Nicolau, Andressa dos S.; Schirru, Roberto; Lima, Alan M.M. de, E-mail: andressa@lmp.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Programa de Engenharia Nuclear
2017-07-01
Quantum Particle Swarm Optimization (QPSO) is a global convergence algorithm that combines the classical PSO philosophy and quantum mechanics to improve performance of PSO. Different from PSO it only has the 'measurement' of the position equation for all particles. The process of 'measurement' in quantum mechanics, obey classic laws while the particle itself follows the quantum rules. QPSO works like PSO in search ability but has fewer parameters control. In order to improve the QPSO performance, some strategies have been proposed in the literature. Weighted QPSO (WQPSO) is a version of QPSO, where weight parameter is insert in the calculation of the balance between the global and local searching of the algorithm. It has been shown to perform well in finding the optimal solutions for many optimization problems. In this article random confinement was introduced in WQPSO. The WQPSO with random confinement was tested in two combinatorial problems. First, we execute the model on Travelling Salesman Problem (TSP) to find the parameters' values resulting in good solutions in general. Finally, the model was tested on Nuclear Reactor Reload Problem, and the performance was compared with QPSO standard. (author)
Quantum particle swarm approaches applied to combinatorial problems
International Nuclear Information System (INIS)
Nicolau, Andressa dos S.; Schirru, Roberto; Lima, Alan M.M. de
2017-01-01
Quantum Particle Swarm Optimization (QPSO) is a global convergence algorithm that combines the classical PSO philosophy and quantum mechanics to improve performance of PSO. Different from PSO it only has the 'measurement' of the position equation for all particles. The process of 'measurement' in quantum mechanics, obey classic laws while the particle itself follows the quantum rules. QPSO works like PSO in search ability but has fewer parameters control. In order to improve the QPSO performance, some strategies have been proposed in the literature. Weighted QPSO (WQPSO) is a version of QPSO, where weight parameter is insert in the calculation of the balance between the global and local searching of the algorithm. It has been shown to perform well in finding the optimal solutions for many optimization problems. In this article random confinement was introduced in WQPSO. The WQPSO with random confinement was tested in two combinatorial problems. First, we execute the model on Travelling Salesman Problem (TSP) to find the parameters' values resulting in good solutions in general. Finally, the model was tested on Nuclear Reactor Reload Problem, and the performance was compared with QPSO standard. (author)
Problems and solutions in quantum chemistry and physics
Johnson, Charles S
1988-01-01
Unusually varied problems, with detailed solutions, cover quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, more. 280 problems, plus 139 supplementary exercises.
Quantum ergodicity in a quantum measure algebra
International Nuclear Information System (INIS)
Stechel, E.B.
1986-01-01
This paper is divided into two parts. Part I assembles three pieces of background necessary to develop the logic behind this result. Section IA is devoted to classical algebraic ergodic theory (AET). Section IB briefly discusses random matrix theory (RMT) which should require very little development since a large fraction of this volume is devoted to this subject. Section IC reviews the concepts in quantum ''phase'' space flow (P(a,b)'s and p/sub n//sup a/'s). Part II develops what the authors will call quantum AET (the quantum analog of classical AET). Section IIA presents the formal development with the new definitions. Section IIB discusses intensity fluctuations in quantum ergodic (QE) spectra, leading to the somewhat surprising result that in a QE system a pure, real, smooth state samples only about 1/3 of its available space
Quantum learning by measurement and feedback
DEFF Research Database (Denmark)
Gammelmark, Søren; Mølmer, Klaus
2009-01-01
We investigate an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom. The capability of the quantum computer to perform desired tasks is monitored by measurements of the output and gradually improved by successive feedback modifications...
Quantum Learning by Measurement and Feedback
DEFF Research Database (Denmark)
Gammelmark, Søren
We investigate an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom. The capability of the quantum computer to perform desired tasks is monitored by measurements of the output and gradually improved by successive feedback modifications...
Optimal control of quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Egger, Daniel; Wilhelm, Frank [Theoretical Physics, Saarland University, 66123 Saarbruecken (Germany)
2015-07-01
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a measurement pulse for superconducting phase qubits. We show how this technique can lead to large measurement contrast close to 99%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2% contrast.
Geometric measure of quantum discord and total quantum correlations in an N-partite quantum state
International Nuclear Information System (INIS)
Hassan, Ali Saif M; Joag, Pramod S
2012-01-01
Quantum discord, as introduced by Ollivier and Zurek (2001 Phys. Rev. Lett. 88 017901), is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic et al (2010 Phys. Rev. Lett. 105 190502) who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu (2010 Phys. Rev. A 82 034302) introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in an N-qubit quantum state. The exact formulas for the N-qubit quantum state can be used to get experimental estimates of the quantum discord and the total quantum correlation. (paper)
Computational approach to large quantum dynamical problems
International Nuclear Information System (INIS)
Friesner, R.A.; Brunet, J.P.; Wyatt, R.E.; Leforestier, C.; Binkley, S.
1987-01-01
The organizational structure is described for a new program that permits computations on a variety of quantum mechanical problems in chemical dynamics and spectroscopy. Particular attention is devoted to developing and using algorithms that exploit the capabilities of current vector supercomputers. A key component in this procedure is the recursive transformation of the large sparse Hamiltonian matrix into a much smaller tridiagonal matrix. An application to time-dependent laser molecule energy transfer is presented. Rate of energy deposition in the multimode molecule for systematic variations in the molecular intermode coupling parameters is emphasized
Function Package for Computing Quantum Resource Measures
Huang, Zhiming
2018-05-01
In this paper, we present a function package for to calculate quantum resource measures and dynamics of open systems. Our package includes common operators and operator lists, frequently-used functions for computing quantum entanglement, quantum correlation, quantum coherence, quantum Fisher information and dynamics in noisy environments. We briefly explain the functions of the package and illustrate how to use the package with several typical examples. We expect that this package is a useful tool for future research and education.
Cavity QED experiments, entanglement and quantum measurement
International Nuclear Information System (INIS)
Brune, M.
2001-01-01
This course is devoted to the physics of entanglement in microwave CQED (cavity quantum electrodynamics) experiments. The heart of this system is a microwave photon trap, made of superconducting mirrors, which stores a few-photon field in a small volume of space for times as long as milliseconds. This field interacts with circular Rydberg atoms injected one by one into the cavity. Section 2 is devoted to the description of the strong coupling regime in Rydberg atom CQED. The tools of the experiment are briefly presented at the beginning of this section as well as the main characteristics of the strong coupling regime. We then show in section 3 how to use the strong interaction with a single photon to perform a non-destructive detection of a single photon with a single atom as a meter. In section 4, we show that the achieved QND (quantum non-demolition) measurement process corresponds to the operation of a quantum phase gate. It allows, in principle, to prepare arbitrary atom + field entangled states. Various methods will be presented for preparing entangled states such as a two atom EPR (Einstein Podolsky Rosen) pair as well as a GHZ triplet. Entanglement involving more and more complex systems will then be investigated in section 5 where the preparation of a ''Schroedinger cat state'' of the cavity field is presented. We especially address in this last section the problem of entanglement between the system and the meter which occurs during any quantum measurement process
Quantum probabilities of composite events in quantum measurements with multimode states
International Nuclear Information System (INIS)
Yukalov, V I; Sornette, D
2013-01-01
The problem of defining quantum probabilities of composite events is considered. This problem is of great importance for the theory of quantum measurements and for quantum decision theory, which is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. Special attention is paid to the application of the approach to systems with multimode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes. (paper)
Quantum theory of measurements as quantum decision theory
International Nuclear Information System (INIS)
Yukalov, V I; Sornette, D
2015-01-01
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device
How much a quantum measurement is informative?
Energy Technology Data Exchange (ETDEWEB)
Dall' Arno, Michele [Graduate School of Information Science, Nagoya University, Nagoya, 464-8601 (Japan); ICFO-Institut de Ciencies Fotoniques, E-08860 Castelldefels, Barcelona (Spain); Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia (Italy); D' Ariano, Giacomo Mauro [Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Gruppo IV, via Bassi 6, I-27100 Pavia (Italy); Sacchi, Massimiliano F. [Quit Group, Dipartimento di Fisica, via Bassi 6, I-27100 Pavia, Italy and Istituto di Fotonica e Nanotecnologie (INF-CNR), P.zza L. da Vinci 32, I-20133, Milano (Italy)
2014-12-04
The informational power of a quantum measurement is the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We discuss its main properties. Informational power is an additive quantity, being equivalent to the classical capacity of a quantum-classical channel. The informational power of a quantum measurement is the maximum of the accessible information of a quantum ensemble that depends on the measurement. We present some examples where the symmetry of the measurement allows to analytically derive its informational power.
Boolean Approach to Dichotomic Quantum Measurement Theories
Energy Technology Data Exchange (ETDEWEB)
Nagata, K. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Nakamura, T. [Keio University, Yokohama (Japan); Batle, J. [Universitat de les Illes Balears, Balearic Islands (Spain); Abdalla, S. [King Abdulaziz University Jeddah, Jeddah (Saudi Arabia); Farouk, A. [Al-Zahra College for Women, Muscat (Egypt)
2017-02-15
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or −1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
Improving Students' Understanding of Quantum Measurement
International Nuclear Information System (INIS)
Zhu Guangtian; Singh, Chandralekha
2010-01-01
We describe the difficulties advanced undergraduate and graduate students have with quantum measurement. To reduce these difficulties, we have developed research-based learning tools such as the Quantum Interactive Learning Tutorial (QuILT) and peer instruction tools. A preliminary evaluation shows that these learning tools are effective in improving students' understanding of concepts related to quantum measurement.
Categorization of Quantum Mechanics Problems by Professors and Students
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Quantum measurement with a positive operator-valued measure
International Nuclear Information System (INIS)
Brandt, Howard E
2003-01-01
In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated
Bohmian mechanics, open quantum systems and continuous measurements
Nassar, Antonio B
2017-01-01
This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from th...
Quantum noise, quantum measurement, and squeezing
International Nuclear Information System (INIS)
Haus, Herman A
2004-01-01
This is the edited text of the Keynote Speech that Professor Haus had been invited to give at the Conference on Fluctuations and Noise in Photonics and Quantum Optics, held at Santa Fe, NM, on 1-4 June 2003. He introduces it as partly an overview, partly a retrospective, finishing with some remarks about the future, addressing the topics as he knew them best, from his own perspective. Sadly, Professor Haus died shortly before he was due to present this speech to conference delegates. (keynote speech)
Simulating quantum correlations as a distributed sampling problem
International Nuclear Information System (INIS)
Degorre, Julien; Laplante, Sophie; Roland, Jeremie
2005-01-01
It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, postselection or nonlocal boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a nonlocal box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states
Quantum probability measures and tomographic probability densities
Amosov, GG; Man'ko, [No Value
2004-01-01
Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the
Measurement analysis and quantum gravity
International Nuclear Information System (INIS)
Albers, Mark; Kiefer, Claus; Reginatto, Marcel
2008-01-01
We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments which speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.
Quantum evolution by discrete measurements
International Nuclear Information System (INIS)
Roa, L; Guevara, M L Ladron de; Delgado, A; Olivares-RenterIa, G; Klimov, A B
2007-01-01
In this article we review two ways of driving a quantum system to a known pure state via a sequence discrete of von Neumann measurements. The first of them assumes that the initial state of the system is unknown, and the evolution is attained only with the help of two non-commuting observables. For this method, the overall success probability is maximized when the eigentstates of the involved observables constitute mutually unbiased bases. The second method assumes the initial state is known and it uses N observables which are consecutively measured to make the state of the system approach the target state. The probability of success of this procedure converges to 1 as the number of observables increases
Quantum evolution by discrete measurements
Energy Technology Data Exchange (ETDEWEB)
Roa, L [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Guevara, M L Ladron de [Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta (Chile); Delgado, A [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Olivares-RenterIa, G [Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile); Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico)
2007-10-15
In this article we review two ways of driving a quantum system to a known pure state via a sequence discrete of von Neumann measurements. The first of them assumes that the initial state of the system is unknown, and the evolution is attained only with the help of two non-commuting observables. For this method, the overall success probability is maximized when the eigentstates of the involved observables constitute mutually unbiased bases. The second method assumes the initial state is known and it uses N observables which are consecutively measured to make the state of the system approach the target state. The probability of success of this procedure converges to 1 as the number of observables increases.
An implementation problem for boson fields and quantum Girsanov transform
Energy Technology Data Exchange (ETDEWEB)
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763 (Korea, Republic of); Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp [Graduate School of Information Sciences, Tohoku University, Sendai 980-8579 (Japan)
2016-08-15
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
An implementation problem for boson fields and quantum Girsanov transform
International Nuclear Information System (INIS)
Ji, Un Cig; Obata, Nobuaki
2016-01-01
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
Research program with no ''measurement problem''
International Nuclear Information System (INIS)
Noyes, H.P.; Gefwert, C.; Manthey, M.J.
1985-07-01
The ''measurement problem'' of contemporary physics is met by recognizing that the physicist participates when constructing and when applying the theory consisting of the formulated formal and measurement criteria (the expressions and rules) providing the necessary conditions which allow him to compute and measure facts, yet retains objectivity by requiring that these criteria, rules and facts be in corroborative equilibrium. We construct the particulate states of quantum physics by a recursive program which incorporates the non-determinism born of communication between asynchronous processes over a shared memory. Their quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar, and m/sub p/ or (not ''and'') G. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact
Students' Epistemological Framing in Quantum Mechanics Problem Solving
Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.
2017-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…
The problem of time quantum mechanics versus general relativity
Anderson, Edward
2017-01-01
This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon ...
Solutions to selected exercise problems in quantum chemistry and spectroscopy
DEFF Research Database (Denmark)
Spanget-Larsen, Jens
2016-01-01
Suggested solutions to a number of problems from the collection "Exercise Problems in Quantum Chemistry and Spectroscopy", previously published on ResearchGate (DOI: 10.13140/RG.2.1.4024.8162).......Suggested solutions to a number of problems from the collection "Exercise Problems in Quantum Chemistry and Spectroscopy", previously published on ResearchGate (DOI: 10.13140/RG.2.1.4024.8162)....
Measures and applications of quantum correlations
International Nuclear Information System (INIS)
Adesso, Gerardo; Bromley, Thomas R; Cianciaruso, Marco
2016-01-01
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role. (topical review)
International Nuclear Information System (INIS)
Gibbons, G. W.; Turok, Neil
2008-01-01
The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a 'magnetic flux' of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat Friedmann-Lemaitre-Robertson-Walker universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for N e-folds of inflation in single-field, slow-roll models is suppressed by of order exp(-3N) and we discuss the implications of this result.
Thermodynamics of Weakly Measured Quantum Systems.
Alonso, Jose Joaquin; Lutz, Eric; Romito, Alessandro
2016-02-26
We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-12-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
International Nuclear Information System (INIS)
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
2012-01-01
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Invariant measures on multimode quantum Gaussian states
Energy Technology Data Exchange (ETDEWEB)
Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)
2012-12-15
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.
Maxwell's demon, Szilard's engine and quantum measurements
International Nuclear Information System (INIS)
Zorek, W.H.
1986-01-01
The author proposes and analyzes a quantum version of Szilard's one-molecule engine. In particular, the author recovers, in the quantum context, Szilard's conclusion concerning the free energy ''cost'' of measurements (delta /sub F/ is greater than or equal to k/sub b/T1n2) per bit of information. A cycle of Szilard's engine is illustrated for both the original and quantum versions. The measurement of the location of the molecule is essential in the process of extracting work in both classical and quantum design. Measurements are made by the classical Maxwell's demon
Quantum mechanics with spontaneous localization and the quantum theory of measurement
International Nuclear Information System (INIS)
Benatti, F.; Ghirardi, G.C.; Rimini, A.; Weber, T.
1986-10-01
Recently a modification of quantum dynamics allowing a unified description of microscopic and macroscopic systems has been introduced. We investigate here the consequences of this approach for the measurement problem. We show that in this way one gets a consistent and objective solution of the problem of the wave packet reduction. (author)
Testing quantum contextuality. The problem of compatibility
International Nuclear Information System (INIS)
Szangolies, Jochen
2015-01-01
Jochen Szangolies contributes a novel way of dealing with the problem of the experimental testability of the Kochen-Specker theorem posed by realistic, that is, noisy, measurements. Such noise spoils perfect compatibility between successive measurements, which however is a necessary requirement to test the notion of contextuality in usual approaches. To overcome this difficulty, a new, extended notion of contextuality that reduces to Kochen-Specker contextuality in the limit of perfect measurement implementations is proposed by the author, together with a scheme to test this notion experimentally. Furthermore, the behaviour of these tests under realistic noise conditions is investigated.
Continuous-Variable Quantum Computation of Oracle Decision Problems
Adcock, Mark R. A.
Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. In the infinite-dimensional case, we study continuous-variable quantum algorithms for the solution of the Deutsch--Jozsa oracle decision problem implemented within a single harmonic-oscillator. Orthogonal states are used as the computational bases, and we show that, contrary to a previous claim in the literature, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform. We further demonstrate that orthogonal encoding bases are not unique, and using the coherent states of the harmonic oscillator as the computational bases, our formalism enables quantifying
From quantum measurement to biology via retrocausality.
Matsuno, Koichiro
2017-12-01
A reaction cycle in general or a metabolic cycle in particular owes its evolutionary emergence to the covering reaction environment acting as a measurement apparatus of a natural origin. The quantum measurement of the environmental origin underlying the molecular processes observed in the biological realm is operative cohesively between the measuring and the measured. The measuring part comes to pull in a quantum as an indivisible lump available from an arbitrary material body to be measured. The inevitable difference between the impinging quantum upon the receiving end on the part of the environment and the actual quantum pulled into the receiving end comes to effectively be nullified through the retrocausative propagation of the corresponding wave function proceeding backwards in time. The retrocausal regulation applied to the interface between the measuring and the measured is to function as the organizational agency supporting biology, and is sought in the act for the present in the immediate future within the realm of quantum phenomena. Molecular dynamics in biology owes both the evolutionary buildup and maintenance of its organization to the retrocausal operation of the unitary transformation applied to quantum phenomena proceeding backwards in time. Quantum measurement provides the cohesive agency that is pivotal for implementing the retrocausal regulation. In particular, the physical origin of Darwinian natural selection can be seen in the retrocausal regulation applied to the unitary transformation of a quantum origin. Copyright © 2017 Elsevier Ltd. All rights reserved.
The entropic cost of quantum generalized measurements
Mancino, Luca; Sbroscia, Marco; Roccia, Emanuele; Gianani, Ilaria; Somma, Fabrizia; Mataloni, Paolo; Paternostro, Mauro; Barbieri, Marco
2018-03-01
Landauer's principle introduces a symmetry between computational and physical processes: erasure of information, a logically irreversible operation, must be underlain by an irreversible transformation dissipating energy. Monitoring micro- and nano-systems needs to enter into the energetic balance of their control; hence, finding the ultimate limits is instrumental to the development of future thermal machines operating at the quantum level. We report on the experimental investigation of a lower bound to the irreversible entropy associated to generalized quantum measurements on a quantum bit. We adopted a quantum photonics gate to implement a device interpolating from the weakly disturbing to the fully invasive and maximally informative regime. Our experiment prompted us to introduce a bound taking into account both the classical result of the measurement and the outcoming quantum state; unlike previous investigation, our entropic bound is based uniquely on measurable quantities. Our results highlight what insights the information-theoretic approach provides on building blocks of quantum information processors.
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Quantum qubit measurement by a quantum point contact with a quantum Langevin equation approach
International Nuclear Information System (INIS)
Dong, Bing; Lei, X.L.; Horing, N.J.M.; Cui, H.L.
2007-01-01
We employ a microscopic quantum Heisenberg-Langevin equation approach to establish a set of quantum Bloch equations for a two-level system (coupled quantum dots) capacitively coupled to a quantum point contact (QPC). The resulting Bloch equations facilitate our analysis of qubit relaxation and decoherence in coupled quantum dots induced by measurement processes at arbitrary bias-voltage and temperature. We also examine the noise spectrum of the meter output current for a symmetric qubit. These results help resolve a recent debate about a quantum oscillation peak in the noise spectrum. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
A Quantum Approach to Subset-Sum and Similar Problems
Daskin, Ammar
2017-01-01
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed-up over the classical algorithms may be possible. We give a numerical example and discuss the complexity of the approach and its further application to the knapsack problem.
The role of measurement in quantum games
International Nuclear Information System (INIS)
Nawaz, Ahmad; Toor, A H
2006-01-01
The game of prisoner dilemma is analysed to study the role of measurement basis in quantum games. Four different types of payoffs for quantum games are identified on the basis of different combinations of initial state and measurement basis. A relation among these different payoffs is established
'quantumness' measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...
Canonical transformations in problems of quantum statistical mechanics
International Nuclear Information System (INIS)
Sankovich, D.P.
1985-01-01
The problem of general canonical transformations in quantum systems possessing a classical analog is considered. The main role plays the Weyl representation of dynamic variables of the quantum system considered. One managed to build a general diagram of canonical transformations in a quantum case and to develop a method for reducing one or another operator to the simplest canonical form. In this case the procedure, being analogous to the Poincare-Birkhof normalization based on the Lie series theory, occurs
The Measurement Problem: Decoherence and Convivial Solipsism
Zwirn, Hervé
2016-06-01
The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve (or to dissolve) it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. The phenomenon of decoherence is often presented as a solution lying inside the pure quantum formalism and not demanding any particular philosophical assumption. Nevertheless, a widely debated question is to decide between two different interpretations. The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate. For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed, so explaining the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears. In this case, explaining why only one single definite outcome is observed remains to do. In this paper, I examine the arguments that have been given for and against both interpretations and defend a new position, the "Convivial Solipsism", according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett's interpretation and sharing also some similarities with Rovelli's relational interpretation and Quantum Bayesianism. I also show how "Convivial Solipsism" can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics.
Quantum algorithms for the ordered search problem via semidefinite programming
International Nuclear Information System (INIS)
Childs, Andrew M.; Landahl, Andrew J.; Parrilo, Pablo A.
2007-01-01
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log 2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log 605 N≅0.433 log 2 N queries, which improves upon the previously best known exact algorithm
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…
Quantum iterative deepening with an application to the halting problem.
Directory of Open Access Journals (Sweden)
Luís Tarrataca
Full Text Available Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of quantum computational models to operate on a superposition of states requires an alternative approach. From a quantum perspective, any measurement of an equivalent halt qubit would have the potential to inherently interfere with the computation by provoking a random collapse amongst the states. This issue is exacerbated by undecidable problems such as the Entscheidungsproblem which require universal computational models, e.g. the classical Turing machine, to be able to proceed indefinitely. In this work we present an alternative view of quantum computation based on production system theory in conjunction with Grover's amplitude amplification scheme that allows for (1 a detection of halt states without interfering with the final result of a computation; (2 the possibility of non-terminating computation and (3 an inherent speedup to occur during computations susceptible of parallelization. We discuss how such a strategy can be employed in order to simulate classical Turing machines.
Quantum Iterative Deepening with an Application to the Halting Problem
Tarrataca, Luís; Wichert, Andreas
2013-01-01
Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of quantum computational models to operate on a superposition of states requires an alternative approach. From a quantum perspective, any measurement of an equivalent halt qubit would have the potential to inherently interfere with the computation by provoking a random collapse amongst the states. This issue is exacerbated by undecidable problems such as the Entscheidungsproblem which require universal computational models, e.g. the classical Turing machine, to be able to proceed indefinitely. In this work we present an alternative view of quantum computation based on production system theory in conjunction with Grover's amplitude amplification scheme that allows for (1) a detection of halt states without interfering with the final result of a computation; (2) the possibility of non-terminating computation and (3) an inherent speedup to occur during computations susceptible of parallelization. We discuss how such a strategy can be employed in order to simulate classical Turing machines. PMID:23520465
Continuous quantum measurement and the quantum to classical transition
International Nuclear Information System (INIS)
Bhattacharya, Tanmoy; Habib, Salman; Jacobs, Kurt
2003-01-01
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. 85, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes that affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit: first, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion
Maxwell's Demon, Szilard's Engine and Quantum Measurements
Zurek, Wojciech Hubert
2003-01-01
We propose and analyze a quantum version of Szilard's ``one-molecule engine.'' In particular, we recover, in the quantum context, Szilard's conclusion concerning the free energy ``cost'' of measurements: $\\Delta F \\geq k_B T\\ln2$ per bit of information.
Quantum measurements of atoms using cavity QED
International Nuclear Information System (INIS)
Dada, Adetunmise C.; Andersson, Erika; Jones, Martin L.; Kendon, Vivien M.; Everitt, Mark S.
2011-01-01
Generalized quantum measurements are an important extension of projective or von Neumann measurements in that they can be used to describe any measurement that can be implemented on a quantum system. We describe how to realize two nonstandard quantum measurements using cavity QED. The first measurement optimally and unambiguously distinguishes between two nonorthogonal quantum states. The second example is a measurement that demonstrates superadditive quantum coding gain. The experimental tools used are single-atom unitary operations effected by Ramsey pulses and two-atom Tavis-Cummings interactions. We show how the superadditive quantum coding gain is affected by errors in the field-ionization detection of atoms and that even with rather high levels of experimental imperfections, a reasonable amount of superadditivity can still be seen. To date, these types of measurements have been realized only on photons. It would be of great interest to have realizations using other physical systems. This is for fundamental reasons but also since quantum coding gain in general increases with code word length, and a realization using atoms could be more easily scaled than existing realizations using photons.
Review of the inverse scattering problem at fixed energy in quantum mechanics
Sabatier, P. C.
1972-01-01
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
Lectures on quantum mechanics with problems, exercises and their solutions
Basdevant, Jean-Louis
2016-01-01
The new edition of this remarkable text offers the reader a conceptually strong introduction to quantum mechanics, but goes beyond this to present a fascinating tour of modern theoretical physics. Beautifully illustrated and engagingly written, it starts with a brief overview of diverse topics across physics including nanotechnology, statistical physics, materials science, astrophysics, and cosmology. The core of the book covers both established and emerging aspects of quantum mechanics. A concise introduction to traditional quantum mechanics covers the Schrödinger equation, Hilbert space, the algebra of observables, hydrogen atom, spin and Pauli principle. Modern features of the field are presented by exploring entangled states, Bell's inequality, quantum cryptography, quantum teleportation and quantum mechanics in the universe. This new edition has been enchanced through the addition of numerous problems with detailed solutions, an introduction to the mathematical tools needed and expanded discussion of th...
On some boundary value problems in quantum statistical mechanics
International Nuclear Information System (INIS)
Angelescu, N.
1978-01-01
The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)
Inconclusive quantum measurements and decisions under uncertainty
Yukalov, Vyacheslav; Sornette, Didier
2016-04-01
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.
Inconclusive quantum measurements and decisions under uncertainty
Directory of Open Access Journals (Sweden)
Vyacheslav I. Yukalov
2016-04-01
Full Text Available We give a mathematical definition for the notion of inconclusive quantum measurements.In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy withthe theory of quantum measurements, the inconclusive quantum measurements correspond,in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluationof the considered prospect, and of an attraction factor, characterizing irrational,subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example,we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.
Security problem on arbitrated quantum signature schemes
International Nuclear Information System (INIS)
Choi, Jeong Woon; Chang, Ku-Young; Hong, Dowon
2011-01-01
Many arbitrated quantum signature schemes implemented with the help of a trusted third party have been developed up to now. In order to guarantee unconditional security, most of them take advantage of the optimal quantum one-time encryption based on Pauli operators. However, in this paper we point out that the previous schemes provide security only against a total break attack and show in fact that there exists an existential forgery attack that can validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover security against the proposed attack.
Security problem on arbitrated quantum signature schemes
Energy Technology Data Exchange (ETDEWEB)
Choi, Jeong Woon [Emerging Technology R and D Center, SK Telecom, Kyunggi 463-784 (Korea, Republic of); Chang, Ku-Young; Hong, Dowon [Cryptography Research Team, Electronics and Telecommunications Research Institute, Daejeon 305-700 (Korea, Republic of)
2011-12-15
Many arbitrated quantum signature schemes implemented with the help of a trusted third party have been developed up to now. In order to guarantee unconditional security, most of them take advantage of the optimal quantum one-time encryption based on Pauli operators. However, in this paper we point out that the previous schemes provide security only against a total break attack and show in fact that there exists an existential forgery attack that can validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover security against the proposed attack.
Quantum system lifetimes and measurement perturbations
International Nuclear Information System (INIS)
Najakov, E.
1977-05-01
The recently proposed description of quantum system decay in terms of repeated measurement perturbations is modified. The possibility of retarded reductions to a unique quantum state, due to ineffective localization of the decay products at initial time measurements, is simply taken into account. The exponential decay law is verified again. A modified equation giving the observed lifetime in terms of unperturbed quantum decay law, measurement frequency and reduction law is derived. It predicts deviations of the observed lifetime from the umperturbed one, together with a dependence on experimental procedures. The influence of different model unperturbed decay laws and reduction laws on this effect is studied
A quantum measure of the multiverse
International Nuclear Information System (INIS)
Vilenkin, Alexander
2014-01-01
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ''watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM
A quantum measure of the multiverse
Energy Technology Data Exchange (ETDEWEB)
Vilenkin, Alexander, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2014-05-01
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the ''watcher''). Here I discuss an extension of this probability measure to quantum theory. The proposed extension is gauge-invariant, as is the classical version of this measure. Observations of the watcher are described by a reduced density matrix, and the frequencies of events can be found using the decoherent histories formalism of Quantum Mechanics (adapted to open systems). The quantum watcher measure makes predictions in agreement with the standard Born rule of QM.
Quantum elastic net and the traveling salesman problem
International Nuclear Information System (INIS)
Kostenko, B.F.; Pribis, J.; Yur'ev, M.Z.
2009-01-01
Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows one to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical computers. Similarly, quantum wave packet reduction allows one to devise the Grover search algorithm which outperforms any classical one. In the present paper we argue that the quantum incoherent tunneling can be used for elaboration of new algorithms able to solve some NP-hard problems, such as the traveling Salesman Problem, considered to be intractable in the classical theory of computer computations
Quantum Nanomechanics: State Engineering and Measurement
International Nuclear Information System (INIS)
Woolley, M. J.; Milburn, G. J.; Doherty, A. C.
2011-01-01
There has recently been a surge of interest in the study of mechanical systems near the quantum limit. Such experiments are motivated by both fundamental interest in studying quantum mechanics with macroscopic engineered systems and potential applications as ultra-sensitive transducers, or even in quantum information processing. A particularly promising system is a microwave cavity optomechanical system, in which a nanomechanical resonator is embedded within (and capacitively coupled to) a superconducting microwave cavity. Here we discuss two schemes for the generation and measurement of quantum states of the nanomechanical resonator. A quantum squeezed state may be generated via mechanical parametric amplification, while a number state may be conditionally generated via continuous measurement and feedback control mediated by a superconducting qubit.
Quantum mechanics and the science of measurements
International Nuclear Information System (INIS)
Ramsey, N.F.
1992-01-01
The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10,000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. In popular accounts of quantum mechanics, such great emphases is placed on the Heisenberg Uncertainty Principle that it often appears that the primary effect of quantum mechanics should be to diminish measurement accuracy whereas in most cases it is the validity of quantum mechanics that makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: (1) Existence of discrete quantum states of energy W i . (2) Energy conservation in transitions between two states. (3) Electromagnetic radiation of frequency ν is quantized with energy hν per quantum. (4) The identity principle. (5) The Heisenberg Uncertainty Principle. (6) Addition of probability amplitudes (not probabilities) so P=vertical strokeψ 1 +ψ 2 vertical stroke 2 ≠vertical strokeψ 1 vertical stroke 2 +vertical strokeψ 2 vertical stroke 2 . (7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its affect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems and the identity principle provides meaning and significance to highly precise measurements with quantized systems. These effects are discussed and illustrated. (orig.)
Quantum decision theory as quantum theory of measurement
International Nuclear Information System (INIS)
Yukalov, V.I.; Sornette, D.
2008-01-01
We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems
Quantum speedup in solving the maximal-clique problem
Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang
2018-03-01
The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.
Tuning quantum measurements to control chaos.
Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R
2017-03-20
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.
Classical limit of the quantum inverse scattering problem
International Nuclear Information System (INIS)
Bogdanov, I.V.
1986-01-01
This paper studies the passage to the limit of classical mechanics which is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number 1>0 in the lowest order of perturbation theory. It is shown how in the limit h→0 in the quantum inverse problem the integral Able transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation
Quantum entanglement, indistinguishability, and the absent-minded driver's problem
International Nuclear Information System (INIS)
Cabello, Adan; Calsamiglia, John
2005-01-01
The absent-minded driver's problem illustrates that probabilistic strategies can give higher pay-offs than deterministic ones. We show that there are strategies using quantum entangled states that give even higher pay-offs, both for the original problem and for the generalized version with an arbitrary number of intersections and any possible set of pay-offs
Connes' embedding problem and winning strategies for quantum XOR games
Harris, Samuel J.
2017-12-01
We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
Quantum measurement of coherent tunneling between quantum dots
International Nuclear Information System (INIS)
Wiseman, H. M.; Utami, Dian Wahyu; Sun, He Bi; Milburn, G. J.; Kane, B. E.; Dzurak, A.; Clark, R. G.
2001-01-01
We describe the conditional and unconditional dynamics of two coupled quantum dots when one dot is subjected to a measurement of its occupation number by coupling it to a third readout dot via the Coulomb interaction. The readout dot is coupled to source and drain leads under weak bias, and a tunnel current flows through a single bound state when energetically allowed. The occupation of the quantum dot near the readout dot shifts the bound state of the readout dot from a low conducting state to a high conducting state. The measurement is made by continuously monitoring the tunnel current through the readout dot. We show that there is a difference between the time scale for the measurement-induced decoherence between the localized states of the dots, and the time scale on which the system becomes localized due to the measurement
Classical field approach to quantum weak measurements.
Dressel, Justin; Bliokh, Konstantin Y; Nori, Franco
2014-03-21
By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
The macroscopic harmonic oscillator and quantum measurements
International Nuclear Information System (INIS)
Hayward, R.W.
1982-01-01
A quantum mechanical description of a one-dimensional macroscopic harmonic oscillator interacting with its environment is given. Quasi-coherent states are introduced to serve as convenient basis states for application of a density matrix formalism to characterize the system. Attention is given to the pertinent quantum limits to the precision of measurement of physical observables that may provide some information on the nature of a weak classical force interacting with the oscillator. A number of ''quantum nondemolition'' schemes proposed by various authors are discussed. (Auth.)
Measurements and mathematical formalism of quantum mechanics
Slavnov, D. A.
2007-03-01
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
Measurement of gravity and gauge fields using quantum mechanical probes
International Nuclear Information System (INIS)
Anandan, J.
1986-01-01
The author considers the question of which quantities are observed when the gravitational and gauge fields are measured by a quantum mechanical probe. The motion of a quantum mechanical particle can be constructed, via Huyghens' principle, by the interference of secondary wavelets. Three types of interference phenomena are considered: interference of two coherent beams separated in space-time during part of their motion; interference of two coherent beams which are in the same region in spacetime but differ in energy or mass; and the Josphson effect and its generalization. The author shows how to determine the gravitational field by means of quantum interference. The corresponding problem for gauge fields is treated and a simple proof of the previously proved theorem for the reconstruction of the connection from the holonomy transformations is presented. A heuristic principle for the gravitational interaction of two quantum mechanical particles is formulated which implies the equivalence of inertial and active gravitational masses
Experimental quantum annealing: case study involving the graph isomorphism problem.
Zick, Kenneth M; Shehab, Omar; French, Matthew
2015-06-08
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.
Quantum theory of successive projective measurements
International Nuclear Information System (INIS)
Johansen, Lars M.
2007-01-01
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The complex modification term is a measure of measurement disturbance. A selective phase rotation is needed to obtain the imaginary part. This leads to a complex quasiprobability: The Kirkwood distribution. We show that the Kirkwood distribution contains full information about the state if the two observables are maximal and complementary. The Kirkwood distribution gives another picture of state reduction. In a nonselective measurement, the modification term vanishes. A selective measurement leads to a quantum state as a non-negative conditional probability. We demonstrate the special significance of the Schwinger basis
Measurement device-independent quantum dialogue
Maitra, Arpita
2017-12-01
Very recently, the experimental demonstration of quantum secure direct communication (QSDC) with state-of-the-art atomic quantum memory has been reported (Zhang et al. in Phys Rev Lett 118:220501, 2017). Quantum dialogue (QD) falls under QSDC where the secrete messages are communicated simultaneously between two legitimate parties. The successful experimental demonstration of QSDC opens up the possibilities for practical implementation of QD protocols. Thus, it is necessary to analyze the practical security issues of QD protocols for future implementation. Since the very first proposal for QD by Nguyen (Phys Lett A 328:6-10, 2004), a large number of variants and extensions have been presented till date. However, all of those leak half of the secret bits to the adversary through classical communications of the measurement results. In this direction, motivated by the idea of Lo et al. (Phys Rev Lett 108:130503, 2012), we propose a measurement device-independent quantum dialogue scheme which is resistant to such information leakage as well as side-channel attacks. In the proposed protocol, Alice and Bob, two legitimate parties, are allowed to prepare the states only. The states are measured by an untrusted third party who may himself behave as an adversary. We show that our protocol is secure under this adversarial model. The current protocol does not require any quantum memory, and thus, it is inherently robust against memory attacks. Such robustness might not be guaranteed in the QSDC protocol with quantum memory (Zhang et al. 2017).
Unary probabilistic and quantum automata on promise problems
Gainutdinova, Aida; Yakaryilmaz, Abuzer
2015-01-01
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs ...
Macroscopic realism and quantum measurement: measurers as a natural kind
International Nuclear Information System (INIS)
Jaeger, Gregg
2014-01-01
The notion of macroscopic realism has been used in attempts to achieve consistency between physics and everyday experience and to locate some boundary between the realms of classical mechanics and quantum meachanics. Its ostensibly underlying conceptual components, realism and macroscopicity, have most often appeared in the foundations of physics in relation to quantum measurement: reality became a prominent topic of discussion in quantum physics after the notion of element of reality was defined and used by Einstein, Podolsky and Rosen in that context, and macroscopicity is often explicitly assumed to be an essential property of any measuring apparatus. However, macroscopicity turns out to be a rather vaguer and less consistently understood notion than typically assumed by physicists who have not explicitly explored the notion themselves. For this reason, it behooves those investigating the foundations of quantum mechanics from a realist perspective to look for alternative notions for grounding quantum measurement. Here, the merits of treating the measuring instrument as a ‘natural kind’ as a means of avoiding anthropocentrism in the foundations of quantum measurement are pointed out as a means of advancing quantum measurement theory. (paper)
The problems of mapping in quantum systems
International Nuclear Information System (INIS)
Xu Gongou; Wang Wenge; Yang Yadian; Fu Deji
1992-01-01
The mapping from the state of Hamiltonian H(0) to that of H(λ) = H(0) + λ(H-H(0)) is established by means of Wigner-Brillion perturbation formula. An iterative perturbation calculation can be carried out to find the stable points set and to show that under what condition the iterative calculation is divergent(non convergent). Avoided crossing point is really a singularity-point showed clearly in such procedure. The topological invariant subspace endowed by corresponding Hamiltonian H(0) is destroyed after such avoided crossing point. It is similar to the classical invariant tori destruction. A quantum KAM theorem can be established in this manner. Numerical results of certain schematic systems are given as illustration
Solution of certain problems in quantum mechanics
Bolotin, A; Raudeliunas, A
2018-01-01
Intended for advanced undergraduates and graduate students in mathematics, physics, and chemistry, this concise treatment demonstrates the theory of special functions' use and application to problems in atomic and molecular physics. 2017 edition.
Parametric description of the quantum measurement process
Liuzzo-Scorpo, P.; Cuccoli, A.; Verrucchi, P.
2015-08-01
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being considered through the quantum-to-classical crossover. Focusing upon projective measures, and exploiting the connection between large-N quantum theories and the classical limit of related ones, we manage to push our description beyond the pre-measurement step. This allows us to show that the outcome production follows from a global-symmetry breaking, entailing the observed system's state reduction, and that the statistical nature of the process is brought about, together with the Born's rule, by the macroscopic character of the measuring apparatus.
Efficient quantum computing with weak measurements
International Nuclear Information System (INIS)
Lund, A P
2011-01-01
Projective measurements with high quantum efficiency are often assumed to be required for efficient circuit-based quantum computing. We argue that this is not the case and show that the fact that they are not required was actually known previously but was not deeply explored. We examine this issue by giving an example of how to perform the quantum-ordering-finding algorithm efficiently using non-local weak measurements considering that the measurements used are of bounded weakness and some fixed but arbitrary probability of success less than unity is required. We also show that it is possible to perform the same computation with only local weak measurements, but this must necessarily introduce an exponential overhead.
Measurement problem in Program Universe. Revision
International Nuclear Information System (INIS)
Noyes, H.P.; Gefwert, C.; Manthey, M.J.
1985-07-01
The ''measurement problem'' of contemporary physics is in our view an artifact of its philosophical and mathematical underpinnings. We describe a new philosophical view of theory formation, rooted in Wittgenstein, and Bishop's and Martin-Loef's constructivity, which obviates such discussions. We present an unfinished, but very encouraging, theory which is compatible with this philosophical framework. The theory is based on the concepts of counting and combinatorics in the framework provided by the combinatorial hierarchy, a unique hierarchy of bit strings which interact by an operation called discrimination. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact. 15 refs
Measurement problem in Program Universe. Revision
Noyes, H. P.; Gefwert, C.; Manthey, M. J.
1985-07-01
The measurement problem of contemporary physics is in our view an artifact of its philosophical and mathematical underpinnings. We describe a new philosophical view of theory formation, rooted in Wittgenstein, and Bishop's and Martin-Loef's constructivity, which obviates such discussions. We present an unfinished, but very encouraging, theory which is compatible with this philosophical framework. The theory is based on the concepts of counting and combinatorics in the framework provided by the combinatorial hierarchy, a unique hierarchy of bit strings which interact by an operation called discrimination. Measurement criteria incorporate c, h-bar and m/sub p/ or (not and) G. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Advances in quantum mechanics contemporary trends and open problems
Dell'Antonio, Gianfausto
2017-01-01
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
Strategies in a symmetric quantum Kolkata restaurant problem
Sharif, Puya; Heydari, Hoshang
2012-12-01
The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.
Implementation of generalized measurements with minimal disturbance on a quantum computer
International Nuclear Information System (INIS)
Decker, T.; Grassl, M.
2006-01-01
We consider the problem of efficiently implementing a generalized measurement on a quantum computer. Using methods from representation theory, we exploit symmetries of the states we want to identify respectively symmetries of the measurement operators. In order to allow the information to be extracted sequentially, the disturbance of the quantum state due to the measurement should be minimal. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Symposium on Decoherence and No-Signalling : Current Interpretational Problems of Quantum Theory
Wüthrich, Adrian; New vistas on old problems : recent approaches to the foundations of quantum mechanics
2017-01-01
Quantum theory has been a subject of interpretational debates ever since its inception. The Einstein-Podolsky-Rosen paradox, the empirical violation of Bell's inequalities, and recent activities to exploit quantum entanglement for technological innovation only exacerbate a long-standing philosophical debate. Despite no-signaling theorems and theories of decoherence, deep- rooted conflicts between special relativistic principles and observed quantum correlations as well as between definite measurement outcomes and quantum theoretical superpositions persist. This collection of papers, first presented at an international symposium at the University of Bern in 2011, highlights some recent approaches to the old problems of a philosophy of quantum mechanics. The authors address the issues from a variety of perspectives, ranging from variations of causal theory and system theoretic interpretations of the observer to an empirical test of whether entanglement itself can be entangled. The essays demonstrate that the di...
Continuous-time quantum algorithms for unstructured problems
International Nuclear Information System (INIS)
Hen, Itay
2014-01-01
We consider a family of unstructured optimization problems, for which we propose a method for constructing analogue, continuous-time (not necessarily adiabatic) quantum algorithms that are faster than their classical counterparts. In this family of problems, which we refer to as ‘scrambled input’ problems, one has to find a minimum-cost configuration of a given integer-valued n-bit black-box function whose input values have been scrambled in some unknown way. Special cases within this set of problems are Grover’s search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch–Josza problem. We consider a couple of examples in detail. In the first, we provide an O(1) deterministic analogue quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant (gives 0 on all inputs or 1 on all inputs) or balanced (returns 0 on half the input states and 1 on the other half). We also study one variant of the random energy model, and show that, as one might expect, its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms. (paper)
Two-body quantum mechanical problem on spheres
Shchepetilov, Alexey V.
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Bulgac, Aurel; Carlson, Joseph A.; Engel, Jonathan; Fann, George; Furnstahl, Richard J.; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W.; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Impedance model for quantum-mechanical barrier problems
International Nuclear Information System (INIS)
Nelin, Evgenii A
2007-01-01
Application of the impedance model to typical quantum-mechanical barrier problems, including those for structures with resonant electron tunneling, is discussed. The efficiency of the approach is illustrated. The physical transparency and compactness of the model and its potential as a teaching and learning tool are discussed. (methodological notes)
Uniqueness of inverse scattering problem in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2001-06-01
It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)
Interpreting quantum coherence through a quantum measurement process
Yao, Yao; Dong, G. H.; Xiao, Xing; Li, Mo; Sun, C. P.
2017-11-01
Recently, there has been a renewed interest in the quantification of coherence or other coherencelike concepts within the framework of quantum resource theory. However, rigorously defined or not, the notion of coherence or decoherence has already been used by the community for decades since the advent of quantum theory. Intuitively, the definitions of coherence and decoherence should be two sides of the same coin. Therefore, a natural question is raised: How can the conventional decoherence processes, such as the von Neumann-Lüders (projective) measurement postulation or partially dephasing channels, fit into the bigger picture of the recently established theoretical framework? Here we show that the state collapse rules of the von Neumann or Lüders-type measurements, as special cases of genuinely incoherent operations (GIOs), are consistent with the resource theories of quantum coherence. New hierarchical measures of coherence are proposed for the Lüders-type measurement and their relationship with measurement-dependent discord is addressed. Moreover, utilizing the fixed-point theory for C* algebra, we prove that GIOs indeed represent a particular type of partially dephasing (phase-damping) channels which have a matrix representation based on the Schur product. By virtue of the Stinespring dilation theorem, the physical realizations of incoherent operations are investigated in detail and we find that GIOs in fact constitute the core of strictly incoherent operations and generally incoherent operations and the unspeakable notion of coherence induced by GIOs can be transferred to the theories of speakable coherence by the corresponding permutation or relabeling operators.
Measurement-device-independent quantum digital signatures
Puthoor, Ittoop Vergheese; Amiri, Ryan; Wallden, Petros; Curty, Marcos; Andersson, Erika
2016-08-01
Digital signatures play an important role in software distribution, modern communication, and financial transactions, where it is important to detect forgery and tampering. Signatures are a cryptographic technique for validating the authenticity and integrity of messages, software, or digital documents. The security of currently used classical schemes relies on computational assumptions. Quantum digital signatures (QDS), on the other hand, provide information-theoretic security based on the laws of quantum physics. Recent work on QDS Amiri et al., Phys. Rev. A 93, 032325 (2016);, 10.1103/PhysRevA.93.032325 Yin, Fu, and Zeng-Bing, Phys. Rev. A 93, 032316 (2016), 10.1103/PhysRevA.93.032316 shows that such schemes do not require trusted quantum channels and are unconditionally secure against general coherent attacks. However, in practical QDS, just as in quantum key distribution (QKD), the detectors can be subjected to side-channel attacks, which can make the actual implementations insecure. Motivated by the idea of measurement-device-independent quantum key distribution (MDI-QKD), we present a measurement-device-independent QDS (MDI-QDS) scheme, which is secure against all detector side-channel attacks. Based on the rapid development of practical MDI-QKD, our MDI-QDS protocol could also be experimentally implemented, since it requires a similar experimental setup.
Quantum measure of nonclassical light
International Nuclear Information System (INIS)
Kim, Ki Sik
2003-01-01
The nonclassical light and its properties are reviewed in the phase space representation. The quantitative measure of nonclassicality for a single-mode case is introduced and its physical significance is discussed in terms of the environmental effects on nonclassicality. The quantitative measure of nonclassical property is defined and used to classify the different nonclassical properties. The nonclassical measure is also extended to the multi-mode case. One of the distinctive features of multi-mode nonclassical light is entanglement, which is not possessed by a single-mode light, and the multi-mode nonclassical measure may reflect the contents of entanglement. The multi-mode nonclassical measure is calculated for the superposition through a beam spitter and compared with the single-mode nonclassical measure.
Numerical and analytical solutions for problems relevant for quantum computers
International Nuclear Information System (INIS)
Spoerl, Andreas
2008-01-01
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
International Nuclear Information System (INIS)
Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge
2004-01-01
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a 'clock'. Conditional probabilities are computed for variables of the system to take certain values when the 'clock' specifies a certain time. This framework is attractive in contexts where the assumption of usual quantum mechanics of the existence of an external, perfectly classical clock, appears unnatural, as in quantum cosmology. Until recently, there were problems with such constructions in ordinary quantum mechanics with additional difficulties in the context of constrained theories like general relativity. A scheme we recently introduced to consistently discretize general relativity removed such obstacles. Since the clock is now an object subject to quantum fluctuations, the resulting evolution in time is not exactly unitary and pure states decohere into mixed states. Here we work out in detail the type of decoherence generated, and we find it to be of Lindblad type. This is attractive since it implies that one can have loss of coherence without violating the conservation of energy. We apply the framework to a simple cosmological model to illustrate how a quantitative estimate of the effect could be computed. For most quantum systems it appears to be too small to be observed, although certain macroscopic quantum systems could in the future provide a testing ground for experimental observation
Quantum measurement and entanglement of spin quantum bits in diamond
Pfaff, W.
2013-01-01
This thesis presents a set of experiments that explore the possible realisation of a macroscopic quantum network based on solid-state quantum bits. Such a quantum network would allow for studying quantum mechanics on large scales (meters, or even kilometers), and can open new possibilities for
Squeezing more from a quantum nondemolition measurement
DEFF Research Database (Denmark)
Buchler, B.C.; Lam, P.K.; Bachor, H.A.
2002-01-01
We use a stable, 5 dB, amplitude squeezed source for a quantum nondomolition (QND) experiment. The performance of our QND system is enhanced by an electro-optic feedforward loop which improve,, the signal transfer efficiency. At best, we measure a total signal transfer of 1.81 and conditional var...
Team decision problems with classical and quantum signals.
Brandenburger, Adam; La Mura, Pierfrancesco
2016-01-13
We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. © 2015 The Authors.
Three-player quantum Kolkata restaurant problem under decoherence
Ramzan, M.
2013-01-01
Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence ( p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice's payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.
Solved Problems in Quantum and Statistical Mechanics
Cini, Michele; Sbragaglia, Mauro
2012-01-01
This work arises from our teaching this subject during many years. The vast majority of these exercises are the exams we gave to our students in this period. We carefully selected the subjects of the exercises to cover all the material which is most needed and which is treated in the most well known texts on these subjects. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that, from our experience, are found most difficult from the average student. Indeed, several exercises are designed to throw light on aspects of the theory that, for one reason or another, are usually neglected with the result to make the students feel uneasy about them. In fact most students get acquainted just with the more common manipulations, which are illustrated by many examples in textbooks. Our exercises never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from the ...
Problem of quantifying quantum correlations with non-commutative discord
Majtey, A. P.; Bussandri, D. G.; Osán, T. M.; Lamberti, P. W.; Valdés-Hernández, A.
2017-09-01
In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo's measure can result in an overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.
Enhancing robustness of multiparty quantum correlations using weak measurement
International Nuclear Information System (INIS)
Singh, Uttam; Mishra, Utkarsh; Dhar, Himadri Shekhar
2014-01-01
Multipartite quantum correlations are important resources for the development of quantum information and computation protocols. However, the resourcefulness of multipartite quantum correlations in practical settings is limited by its fragility under decoherence due to environmental interactions. Though there exist protocols to protect bipartite entanglement under decoherence, the implementation of such protocols for multipartite quantum correlations has not been sufficiently explored. Here, we study the effect of local amplitude damping channel on the generalized Greenberger–Horne–Zeilinger state, and use a protocol of optimal reversal quantum weak measurement to protect the multipartite quantum correlations. We observe that the weak measurement reversal protocol enhances the robustness of multipartite quantum correlations. Further it increases the critical damping value that corresponds to entanglement sudden death. To emphasize the efficacy of the technique in protection of multipartite quantum correlation, we investigate two proximately related quantum communication tasks, namely, quantum teleportation in a one sender, many receivers setting and multiparty quantum information splitting, through a local amplitude damping channel. We observe an increase in the average fidelity of both the quantum communication tasks under the weak measurement reversal protocol. The method may prove beneficial, for combating external interactions, in other quantum information tasks using multipartite resources. - Highlights: • Extension of weak measurement reversal scheme to protect multiparty quantum correlations. • Protection of multiparty quantum correlation under local amplitude damping noise. • Enhanced fidelity of quantum teleportation in one sender and many receivers setting. • Enhanced fidelity of quantum information splitting protocol
Enhancing robustness of multiparty quantum correlations using weak measurement
Energy Technology Data Exchange (ETDEWEB)
Singh, Uttam, E-mail: uttamsingh@hri.res.in [Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India); Mishra, Utkarsh, E-mail: utkarsh@hri.res.in [Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India); Dhar, Himadri Shekhar, E-mail: dhar.himadri@gmail.com [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India)
2014-11-15
Multipartite quantum correlations are important resources for the development of quantum information and computation protocols. However, the resourcefulness of multipartite quantum correlations in practical settings is limited by its fragility under decoherence due to environmental interactions. Though there exist protocols to protect bipartite entanglement under decoherence, the implementation of such protocols for multipartite quantum correlations has not been sufficiently explored. Here, we study the effect of local amplitude damping channel on the generalized Greenberger–Horne–Zeilinger state, and use a protocol of optimal reversal quantum weak measurement to protect the multipartite quantum correlations. We observe that the weak measurement reversal protocol enhances the robustness of multipartite quantum correlations. Further it increases the critical damping value that corresponds to entanglement sudden death. To emphasize the efficacy of the technique in protection of multipartite quantum correlation, we investigate two proximately related quantum communication tasks, namely, quantum teleportation in a one sender, many receivers setting and multiparty quantum information splitting, through a local amplitude damping channel. We observe an increase in the average fidelity of both the quantum communication tasks under the weak measurement reversal protocol. The method may prove beneficial, for combating external interactions, in other quantum information tasks using multipartite resources. - Highlights: • Extension of weak measurement reversal scheme to protect multiparty quantum correlations. • Protection of multiparty quantum correlation under local amplitude damping noise. • Enhanced fidelity of quantum teleportation in one sender and many receivers setting. • Enhanced fidelity of quantum information splitting protocol.
Work required for selective quantum measurement
Konishi, Eiji
2018-06-01
In quantum mechanics, we define the measuring system M in a selective measurement by two conditions. Firstly, when we define the measured system S as the system in which the non-selective measurement part acts, M is independent from the measured system S as a quantum system in the sense that any time-dependent process in the total system S + M is divisible into parts for S and M. Secondly, when we can separate S and M from each other without changing the unitary equivalence class of the state of S from that obtained by the partial trace of M, the eigenstate selection in the selective measurement cannot be realized. In order for such a system M to exist, we show that in one selective measurement of an observable of a quantum system S 0 of particles in S, there exists a negative entropy transfer from M to S that can be directly transformed into an amount of Helmholtz free energy of where T is the thermodynamic temperature of the system S. Equivalently, an extra amount of work, , is required to be done by the system M.
Quantum metrology foundation of units and measurements
Goebel, Ernst O
2015-01-01
The International System of Units (SI) is the world's most widely used system of measurement, used every day in commerce and science, and is the modern form of the metric system. It currently comprises the meter (m), the kilogram (kg), the second (s), the ampere (A), the kelvin (K), the candela (cd) and the mole (mol)). The system is changing though, units and unit definitions are modified through international agreements as the technology of measurement progresses, and as the precision of measurements improves. The SI is now being redefined based on constants of nature and their realization by quantum standards. Therefore, the underlying physics and technologies will receive increasing interest, and not only in the metrology community but in all fields of science. This book introduces and explains the applications of modern physics concepts to metrology, the science and the applications of measurements. A special focus is made on the use of quantum standards for the realization of the forthcoming new SI (the...
Measurement-Device-Independent Quantum Cryptography
Tang, Zhiyuan
Quantum key distribution (QKD) enables two legitimate parties to share a secret key even in the presence of an eavesdropper. The unconditional security of QKD is based on the fundamental laws of quantum physics. Original security proofs of QKD are based on a few assumptions, e.g., perfect single photon sources and perfect single-photon detectors. However, practical implementations of QKD systems do not fully comply with such assumptions due to technical limitations. The gap between theory and implementations leads to security loopholes in most QKD systems, and several attacks have been launched on sophisticated QKD systems. Particularly, the detectors have been found to be the most vulnerable part of QKD. Much effort has been put to build side-channel-free QKD systems. Solutions such as security patches and device-independent QKD have been proposed. However, the former are normally ad-hoc, and cannot close unidentified loopholes. The latter, while having the advantages of removing all assumptions on devices, is impractical to implement today. Measurement-device-independent QKD (MDI-QKD) turns out to be a promising solution to the security problem of QKD. In MDI-QKD, all security loopholes, including those yet-to-be discovered, have been removed from the detectors, the most critical part in QKD. In this thesis, we investigate issues related to the practical implementation and security of MDI-QKD. We first present a demonstration of polarization-encoding MDI-QKD. Taking finite key effect into account, we achieve a secret key rate of 0.005 bit per second (bps) over 10 km spooled telecom fiber, and a 1600-bit key is distributed. This work, together with other demonstrations, shows the practicality of MDI-QKD. Next we investigate a critical assumption of MDI-QKD: perfect state preparation. We apply the loss-tolerant QKD protocol and adapt it to MDI-QKD to quantify information leakage due to imperfect state preparation. We then present an experimental demonstration of
Quantum broadcasting problem in classical low-power signal processing
International Nuclear Information System (INIS)
Janzing, Dominik; Steudel, Bastian
2007-01-01
We prove a no-broadcasting theorem for the Holevo information of a noncommuting ensemble stating that no operation can generate a bipartite ensemble such that both copies have the same information as the original. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transferring at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy
Quantum N-body problem with a minimal length
International Nuclear Information System (INIS)
Buisseret, Fabien
2010-01-01
The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [x,p]=i(1+βp 2 ), leading to the existence of a minimal observable length √(β). For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of the N-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that in the harmonic oscillator case, the β-dependent term grows faster with increasing N than the β-independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for D-dimensional systems. Consequently, quantum N-body bound states might be interesting places to look at nontrivial manifestations of a minimal length, since the more particles that are present, the more the system deviates from standard quantum-mechanical predictions.
Test-state approach to the quantum search problem
International Nuclear Information System (INIS)
Sehrawat, Arun; Nguyen, Le Huy; Englert, Berthold-Georg
2011-01-01
The search for 'a quantum needle in a quantum haystack' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings - the oracles - is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for 'a classical needle in a classical haystack'. Since the outcome of Grover's algorithm is probabilistic - it gives the correct answer with high probability, not with certainty - the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize 'a classical search for the quantum needle' which is deterministic - it always gives a definite answer after a finite number of steps - and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.
Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.
Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2014-05-22
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.
Quantum disentanglement and phase measurements
International Nuclear Information System (INIS)
Buzek, V.; Hillery, M.
1995-01-01
A 50:50 beam splitter disentangles a two-mode squeezed vacuum state into two single-mode squeezed vacuum states. With the proper choice of parameters these two single-mode states will be identical. If one is passed through a device which shifts its phase, then the phases of the shifted and reference (unshifted) modes can be determined by the Vogel-Schleich technique. In this way the phase difference, i.e. the phase shift, can be measured to an accuracy of 1/N, where N is the total number of photons coming into the beam splitter. An improved scheme is also proposed involving the disentanglement of a shifted two-mode squeezed vacuum state. This leads to two shifted squeezed vacuum states at the output of the beam splitter. If one of these is passed through the phase shifter, then by performing homodyne measurements on the shifted and unshifted modes the phase shift can again be determined to an accuracy of 1/N. (author) 4 figs., 14 refs
Measurement problem in PROGRAM UNIVERSE
International Nuclear Information System (INIS)
Noyes, H.P.; Gefwert, C.
1984-12-01
We present a discrete theory that meets the measurement problem in a new way. We generate a growing universe of bit strings, labeled by 2 127 + 136 strings organized by some representation of the closed, four level, combinatorial hierarchy, of bit-length N 139 greater than or equal to 139. The rest of the strings for each label, which grow in both length and number, are called addresses. The generating algorithm, called PROGRAM UNIVERSE, starts from a random choice between the two symbols ''0'' and ''1'' and grows (a) by discriminating between two randomly chosen strings and adjoining a novel result to the universe, or when the string so generated is not novel, by (b) adjoining a randomly chosen bit at the growing end of each string. We obtain, by appropriate definitions and interpretations, stable ''particles'' which satisfy the usual relativistic kinematics and quantized angular momentum without being localizable in a continuum space-time. The labeling scheme is congruent with the ''standard model'' of quarks and leptons with three generations, but for the problem at hand, the implementation of this aspect of the theory is unimportant. What matters most is that (a) these complicated ''particles'' have the periodicities familiar from relativistic ''deBroglie waves'' and resolve in a discrete way the ''wave-particle dualism'' and (b) can be ''touched'' by our discrete equivalent of ''soft photons'' in such a way as to follow, macroscopically, the usual Rutherford scattering trajectories with the associated bound states. Thus our theory could provide a discrete description of ''measurement'' in a way that allows no conceptual barrier between the ''micro'' and the ''macro'' worlds, if we are willing to base our physics on counting and exclude the ambiguities associated with the unobservable ''continuum''. 27 refs
Quantum method of the inverse scattering problem. Pt. 1
International Nuclear Information System (INIS)
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Relational description of the measurement process in quantum field theory
International Nuclear Information System (INIS)
Gambini, Rodolfo; Porto, Rafael A.
2002-01-01
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse takes place. A suitable use of the causal structure of the devices involved in the measurement process allowed us to introduce a covariant notion for the collapse of quantum states. However, a fully consistent description in the relativistic domain requires the extension of the interpretation to quantum fields. The extension is far from straightforward. Besides the obvious difficulty of dealing with the infinite degrees of freedom of the field theory, one has to analyse the restrictions imposed by causality concerning the allowed operations in a measurement process. In this paper we address these issues. We shall show that, in the case of partial causally connected measurements, our description allows us to include a wider class of causal operations than the one resulting from the standard way of computing conditional probabilities. This alternative description could be experimentally tested. A verification of this proposal would give stronger support to the realistic interpretations of the states in quantum mechanics. (author)
Quantum key distribution without alternative measurements
Cabello, A
2000-01-01
Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used to generate the same sequence of random bits in two remote places. A quantum key distribution protocol based on this idea is described. The scheme exhibits the following features. (a) It does not require that Alice and Bob choose between alternative measurements, therefore improving the rate of generated bits by transmitted qubit. (b) It allows Alice and Bob to generate a key of arbitrary length using a single quantum system (three EPR pairs), instead of a long sequence of them. (c) Detecting Eve requires the comparison of fewer bits. (d) Entanglement is an essential ingredient. The scheme assumes reliable measurements of the Bell operator. (20 refs).
High-rate measurement-device-independent quantum cryptography
DEFF Research Database (Denmark)
Pirandola, Stefano; Ottaviani, Carlo; Spedalieri, Gaetana
2015-01-01
Quantum cryptography achieves a formidable task - the remote distribution of secret keys by exploiting the fundamental laws of physics. Quantum cryptography is now headed towards solving the practical problem of constructing scalable and secure quantum networks. A significant step in this direction...
Channel capacities versus entanglement measures in multiparty quantum states
International Nuclear Information System (INIS)
Sen, Aditi; Sen, Ujjwal
2010-01-01
For quantum states of two subsystems, highly entangled states have a higher capacity of transmitting classical as well as quantum information, and vice versa. We show that this is no more the case in general: Quantum capacities of multiaccess channels, motivated by communication in quantum networks, do not have any relation with genuine multiparty entanglement measures. Importantly, the statement is demonstrated for arbitrary multipartite entanglement measures. Along with revealing the structural richness of multiaccess channels, this gives us a tool to classify multiparty quantum states from the perspective of its usefulness in quantum networks, which cannot be visualized by any genuine multiparty entanglement measure.
Scaling the robustness of the solutions for quantum controllable problems
International Nuclear Information System (INIS)
Kallush, S.; Kosloff, R.
2011-01-01
The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed.
A relativistic theory for continuous measurement of quantum fields
International Nuclear Information System (INIS)
Diosi, L.
1990-04-01
A formal theory for the continuous measurement of relativistic quantum fields is proposed. The corresponding scattering equations were derived. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of this theory. A possible example of the relativistic continuous measurement has been outlined in standard Quantum Electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields. (author) 23 refs
Experimental realization of a one-way quantum computer algorithm solving Simon's problem.
Tame, M S; Bell, B A; Di Franco, C; Wadsworth, W J; Rarity, J G
2014-11-14
We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's problem-a black-box period-finding problem that has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.
Quantum simulation of the integer factorization problem: Bell states in a Penning trap
Rosales, Jose Luis; Martin, Vicente
2018-03-01
The arithmetic problem of factoring an integer N can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of N , are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of N . This is equivalent to a quantum sieve that is shown to require only o (ln√{N}) 3 energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.
A stochastic model for quantum measurement
International Nuclear Information System (INIS)
Budiyono, Agung
2013-01-01
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)
Quantum fluctuation theorems and power measurements
International Nuclear Information System (INIS)
Prasanna Venkatesh, B; Watanabe, Gentaro; Talkner, Peter
2015-01-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics. (paper)
International Nuclear Information System (INIS)
Takeoka, Masahiro; Fujiwara, Mikio; Mizuno, Jun; Sasaki, Masahide
2004-01-01
Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques
On the problem of existence of quantum field theory
International Nuclear Information System (INIS)
Chaichian, M.; Hayashi, M.; Nelipa, N.F.; Pukhov, E.A.
1978-01-01
Existence of quantum field theory is considered for the four-dimensional phi 3 -model. The mathematical tool of contraction mapping principle is used to investigate the question of existence of solution for the infinite system of coupled equations for the Green functions of the theory in the Euclidean region. Formulation of the problem for this model with one divergent part is interesting in itself and provides the first attempt towards the study of other renormalizable quantum field theory models with infinite number of divergent graphs. For sufficiently small values of coupling constant, the theory has a unique solution for the truncated system of equations for the Green functions. However, for the complete, infinite set of equations, the Banach fixed point theorem admits a solution only when the coupling constant tends to zero. Possible reasons for such a result are discussed. (author)
Moment problems and the causal set approach to quantum gravity
International Nuclear Information System (INIS)
Ash, Avner; McDonald, Patrick
2003-01-01
We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle, and a renormalizability condition. The corresponding dynamics are completely determined by a sequence of non-negative real coupling constants. Using techniques related to the classical moment problem, we give a complete description of any such sequence of coupling constants. We prove a representation theorem: every discrete theory of quantum gravity arising from causal set dynamics satisfying covariance, causality, and renormalizability corresponds to a unique probability distribution function on the non-negative real numbers, with the coupling constants defining the theory given by the moments of the distribution
Process tomography via sequential measurements on a single quantum system
CSIR Research Space (South Africa)
Bassa, H
2015-09-01
Full Text Available The authors utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters...
On quantum statistical inference
Barndorff-Nielsen, O.E.; Gill, R.D.; Jupp, P.E.
2003-01-01
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, developments in the theory of quantum measurements have
Quantum Backaction Evading Measurement of Collective Mechanical Modes.
Ockeloen-Korppi, C F; Damskägg, E; Pirkkalainen, J-M; Clerk, A A; Woolley, M J; Sillanpää, M A
2016-09-30
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.
Measurement-Device Independency Analysis of Continuous-Variable Quantum Digital Signature
Directory of Open Access Journals (Sweden)
Tao Shang
2018-04-01
Full Text Available With the practical implementation of continuous-variable quantum cryptographic protocols, security problems resulting from measurement-device loopholes are being given increasing attention. At present, research on measurement-device independency analysis is limited in quantum key distribution protocols, while there exist different security problems for different protocols. Considering the importance of quantum digital signature in quantum cryptography, in this paper, we attempt to analyze the measurement-device independency of continuous-variable quantum digital signature, especially continuous-variable quantum homomorphic signature. Firstly, we calculate the upper bound of the error rate of a protocol. If it is negligible on condition that all measurement devices are untrusted, the protocol is deemed to be measurement-device-independent. Then, we simplify the calculation by using the characteristics of continuous variables and prove the measurement-device independency of the protocol according to the calculation result. In addition, the proposed analysis method can be extended to other quantum cryptographic protocols besides continuous-variable quantum homomorphic signature.
Computational nuclear quantum many-body problem: The UNEDF project
Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.
2013-10-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Problems of quantum electrodynamics with external field creating pairs
International Nuclear Information System (INIS)
Fradkin, E.S.; Gitman, D.M.
1979-11-01
This paper is a preliminary version of a review of the results obtained by the authors and their collaborators which mainly concern problems of quantum electrodynamics with the pair-creating external field. In this paper the Furry picture is constructed for quantum electrodynamics with the pair-creating external field. It is shown, that various Green functions in the external field arise in the theory in a natural way. Special features of usage of the unitarity conditions for calculating the total probabilities of transitions are discussed. Perturbation theory for determining the mean electromagnetic field is constructed. Effective Lagrangians for pair-creating fields are built. One of the possible ways to introduce external field in quantum electrodynamics is considered. All the Green functions arising in the theory suggested are calculated for a constant field and a plane wave field. For the case of the electric field the total probability of creation of pairs from the vacuum accompanied by the photon irradiation and the total probability of transition from a single-electron state accompanied by the photon irradiation and creation of pairs are obtained by using the formulated rules for calculating the total probabilities of transitions. (author)
Classical and nonclassical randomness in quantum measurements
International Nuclear Information System (INIS)
Farenick, Douglas; Plosker, Sarah; Smith, Jerrod
2011-01-01
The space POVM H (X) of positive operator-valued probability measures on the Borel sets of a compact (or even locally compact) Hausdorff space X with values in B(H), the algebra of linear operators acting on a d-dimensional Hilbert space H, is studied from the perspectives of classical and nonclassical convexity through a transform Γ that associates any positive operator-valued measure ν with a certain completely positive linear map Γ(ν) of the homogeneous C*-algebra C(X) x B(H) into B(H). This association is achieved by using an operator-valued integral in which nonclassical random variables (that is, operator-valued functions) are integrated with respect to positive operator-valued measures and which has the feature that the integral of a random quantum effect is itself a quantum effect. A left inverse Ω for Γ yields an integral representation, along the lines of the classical Riesz representation theorem for linear functionals on C(X), of certain (but not all) unital completely positive linear maps φ:C(X) x B(H)→B(H). The extremal and C*-extremal points of POVM H (X) are determined.
A measure theoretical approach to quantum stochastic processes
Energy Technology Data Exchange (ETDEWEB)
Waldenfels, Wilhelm von
2014-04-01
Authored by a leading researcher in the field. Self-contained presentation of the subject matter. Examines a number of worked examples in detail. This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.
A measure theoretical approach to quantum stochastic processes
Von Waldenfels, Wilhelm
2014-01-01
This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.
Reconsideration of the Uncertainty Relations and Quantum Measurements
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available Discussions on uncertainty relations (UR and quantum measurements (QMS persisted until nowadays in publications about quantum mechanics (QM. They originate mainly from the conventional interpretation of UR (CIUR. In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and discussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucialpieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i thought-experimental fictions or (ii simple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an information-transmission model, in which the quantum observables are considered as random variables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.
Reconsideration of the Uncertainty Relations and Quantum Measurements
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available Discussions on uncertainty relations (UR and quantum measurements (QMS persisted until nowadays in publications about quantum mechanics (QM. They originate mainly from the conventional interpretation of UR (CIUR. In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and dis- cussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucial pieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i thought-experimental fictions or (ii sim- ple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an information- transmission model, in which the quantum observables are considered as random vari- ables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.
Measurement-only topological quantum computation via anyonic interferometry
International Nuclear Information System (INIS)
Bonderson, Parsa; Freedman, Michael; Nayak, Chetan
2009-01-01
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems
Quantum measurement and the mind-brain connection
International Nuclear Information System (INIS)
Stapp, H.P.
1990-01-01
It is argued that quantum measurements do pose a problem, within the context created by the fundamental aim of science, which is identified as the construction of a cohesive, comprehensive, and rationally coherent idea of the nature of the world in which we live. Models of nature are divided into two classes: (1), those in which there is a selection process that, for any possible measurement, would, if that measurement were to be performed, pick out one single outcome, and, (2), all others. It is proved that any model of class that reproduces the predictions of quantum theory must violate the condition that there be no faster-than-light influences of any kind. This result is used to motivate the study of models in which unitary evolution is maintained and there is no selection of unique outcomes. A consideration of ontic probabilities, historical records, and the form of the mind-brain connection leads to an elaboration of the Everett many-worlds interpretation that appears to provide the basis of satisfactory solution of the measurement problem. 18 refs
Decoherence assisting a measurement-driven quantum evolution process
International Nuclear Information System (INIS)
Roa, Luis; Olivares-Renteria, G. A.
2006-01-01
We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of two complementary observables
The realism problem of quantum mechanics in view of the decoherence interpretation
International Nuclear Information System (INIS)
Messer, Joachim August
2007-01-01
Quantum mechanics in the conception, as it is today present, contains - what concerns its conceivable understanding and its interpretation - numerous paradoxa. The best known Copenhagen interpretation is critized and other interpretations, as the many-world interpretation and the modern, today mostly attended decoherence interpretation are put to this describingly on side. Axiomatic explanation attempts, like those from Mackey, Jauch, and Piron are analyzed and the measurement problem discussed from three ways of view: the introduction of a cut by Georg Suessmann, the scaling formalism from Klaus Hepp, and the philosophy from Bernulf Kanitschneider. Especially the critique given by Albert Einstein on the Bohr-Heisenberg Copenhagen interpretation and the completeness of a realistic quantum theory by the EPR thought experiment (called from Einstein, Podolsky, and Rosen) is more detailedly studied and extended to a holomorphic realism, in which the measurement quantities become visible as boundary values of a holomorphic function. This analytic continuation throws a new light on the body-soul parallelism, which exceeds the positions of Platon and Feigl. Beside the decoherence also the superselection rules, which are extensively discussed, are an example for a realistic state reduction - however the nonlocality of realistic quantum mechanics forces to a dualism of Higgs' symmetry breaking with local decoherence in the terrestrial laboratory. The position of a holomorphic barycentric realism is worked out by regress to the quantum field theory of Lehmann, Symanzik, and Zimmermann (LSZ) with its reduction formula. Quantum-cosmological implications, non-commutative geometry, K theory, and background field are also discussed. The newly designed knowledge theory of the holomorphic, barycentric realism - which in the classical limit goes over in a critical realism - forms also a bridge to a deepened humanism, which cannot be constructed from purely classical physics. As
A conceptual analysis of quantum zeno; paradox, measurement, and experiment
International Nuclear Information System (INIS)
Home, D.; Whitaker, M.A.
1997-01-01
Arguments on controversial points concerning quantum measurement theory and the quantum Zeno effect are presented. In particular it is argued that (1) the quantum Zeno effect is a genuine result of quantum theory and current quantum measurement theory, independent of the projection postulate; (2) the effect is of very general nature and rests on analogous arguments to those involved in Bell close-quote s theories; (3) the term open-quotes quantum Zeno effectclose quotes may usefully be restricted to experiments where a measuring device exerts a nonlocal negative-result effect on a microscopic system, mere inhibition of a transition by a directly interacting device not qualifying; (4) since no decay is truly exponential, theoretically all decay phenomena should exhibit the quantum Zeno effect under observation, continuous or discrete. A detailed study is made of the experiments claiming to demonstrate the effect; it is found that they do not meet our criterion above. copyright 1997 Academic Press, Inc
Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics
International Nuclear Information System (INIS)
1978-08-01
The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references
The issue of phases in quantum measurement theory
International Nuclear Information System (INIS)
Pati, Arun Kumar
1999-01-01
The issue of phases is always very subtle in quantum world and many of the curious phenomena are due to the existence of the phase of the quantum mechanical wave function. We investigate the issue of phases in quantum measurement theory and predict a new effect of fundamental importance. We call a quantum system under goes a quantum Zeno dynamics when the unitary evolution of a quantum system is interrupted by a sequence of measurements. In particular, we investigate the effect of repeated measurements on the geometric phase and show that the quantum Zeno dynamics can inhibit its development under a large number of measurement pulses. It is interesting to see that neither the total phase nor the dynamical phase goes to zero under large number of measurements. This new effect we call as the 'quantum Zeno Phase effect' in analogous to the quantum Zeno effect where the repeated measurements inhibit the transition probability. This 'quantum Zeno Phase effect' can be proved within von Neumann's collapse mechanism as well as using a continuous measurement model. So the effect is really independent of any particular measurement model considered. Since the geometric phase attributes a memory to a quantum system our results also proves that the path dependent memory of a system can be erased by a sequence of measurements. The quantum Zeno Phase effect provides a way to control and manipulate the phase of a wave function in an interference set up. Finally, we stress that the quantum Zeno Phase effect can be tested using neutron, photon and atom interference experiments with the presently available technology. (Author)
Effective Fault-Tolerant Quantum Computation with Slow Measurements
International Nuclear Information System (INIS)
DiVincenzo, David P.; Aliferis, Panos
2007-01-01
How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability
Measurement of quantum noise in a single-electron transistor near the quantum limit
Xue, W. W.; Ji, Z.; Pan, Feng; Stettenheim, Joel; Blencowe, M. P.; Rimberg, A. J.
2009-09-01
Quantum measurement has challenged physicists for almost a century. Classically, there is no lower bound on the noise a measurement may add. Quantum mechanically, however, measuring a system necessarily perturbs it. When applied to electrical amplifiers, this means that improved sensitivity requires increased backaction that itself contributes noise. The result is a strict quantum limit on added amplifier noise. To approach this limit, a quantum-limited amplifier must possess an ideal balance between sensitivity and backaction; furthermore, its noise must dominate that of subsequent classical amplifiers. Here, we report the first complete and quantitative measurement of the quantum noise of a superconducting single-electron transistor (S-SET) near a double Cooper-pair resonance predicted to have the right combination of sensitivity and backaction. A simultaneous measurement of our S-SET's charge sensitivity indicates that it operates within a factor of 3.6 of the quantum limit, a fourfold improvement over the nearest comparable results.
Dynamics of quantum measurements employing two Curie-Weiss apparatuses
Perarnau-Llobet, Martí; Nieuwenhuizen, Theodorus Maria
2017-10-01
Two types of quantum measurements, measuring the spins of an entangled pair and attempting to measure a spin at either of two positions, are analysed dynamically by apparatuses of the Curie-Weiss type. The outcomes comply with the standard postulates. This article is part of the themed issue `Second quantum revolution: foundational questions'.
Blind topological measurement-based quantum computation.
Morimae, Tomoyuki; Fujii, Keisuke
2012-01-01
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3 × 10(-3), which is comparable to that (7.5 × 10(-3)) of non-blind topological quantum computation. As the error per gate of the order 10(-3) was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.
Coherence and measurement in quantum thermodynamics.
Kammerlander, P; Anders, J
2016-02-26
Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.
Measurement Uncertainty for Finite Quantum Observables
Directory of Open Access Journals (Sweden)
René Schwonnek
2016-06-01
Full Text Available Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method is semidefinite programming, which we apply to arbitrary finite collections of projective observables on a finite dimensional Hilbert space. The quantification of errors is based on an arbitrary cost function, which assigns a penalty to getting result x rather than y, for any pair ( x , y . This induces a notion of optimal transport cost for a pair of probability distributions, and we include an Appendix with a short summary of optimal transport theory as needed in our context. There are then different ways to form an overall figure of merit from the comparison of distributions. We consider three, which are related to different physical testing scenarios. The most thorough test compares the transport distances between the marginals of a joint measurement and the reference observables for every input state. Less demanding is a test just on the states for which a “true value” is known in the sense that the reference observable yields a definite outcome. Finally, we can measure a deviation as a single expectation value by comparing the two observables on the two parts of a maximally-entangled state. All three error quantities have the property that they vanish if and only if the tested observable is equal to the reference. The theory is illustrated with some characteristic examples.
On the problem of time in quantum mechanics
Bauer, M.
2017-05-01
The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured by Heisenberg early on, seemed to exclude the existence of such an operator. However Dirac's formulation of an electron's relativistic QM does allow the introduction of a dynamical time operator that is self-adjoint. Consequently, it can be considered as the generator of a unitary transformation of the system, as well as an additional system observable subject to uncertainty. In the present paper these aspects are examined within the standard framework of relativistic QM.
Directory of Open Access Journals (Sweden)
Tao Zhang
2012-01-01
Full Text Available An elite quantum behaved particle swarm optimization (EQPSO algorithm is proposed, in which an elite strategy is exerted for the global best particle to prevent premature convergence of the swarm. The EQPSO algorithm is employed for solving bilevel multiobjective programming problem (BLMPP in this study, which has never been reported in other literatures. Finally, we use eight different test problems to measure and evaluate the proposed algorithm, including low dimension and high dimension BLMPPs, as well as attempt to solve the BLMPPs whose theoretical Pareto optimal front is not known. The experimental results show that the proposed algorithm is a feasible and efficient method for solving BLMPPs.
Measures of Quantum Synchronization in Continuous Variable Systems
Mari, A.; Farace, A.; Didier, N.; Giovannetti, V.; Fazio, R.
2013-09-01
We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.
Projective measurements in quantum and classical optical systems
CSIR Research Space (South Africa)
Roux, FS
2014-09-01
Full Text Available equally well to both classical and quantum optical systems. A projective measurement, in the context of quantum mechanics, is understood to be the process where a projection operator operates on some input state. Often this projection operator is composed...) Projective measurements in quantum and classical optical systems Filippus S. Roux* and Yingwen Zhang CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa (Received 3 July 2014; published 22 September 2014) Experimental setups for the optical...
Understanding quantum measurement from the solution of dynamical models
Energy Technology Data Exchange (ETDEWEB)
Allahverdyan, Armen E. [Laboratoire de Physique Statistique et Systèmes Complexes, ISMANS, 44 Av. Bartholdi, 72000 Le Mans (France); Balian, Roger [Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette cedex (France); Nieuwenhuizen, Theo M., E-mail: T.M.Nieuwenhuizen@uva.nl [Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, NY 10003 (United States)
2013-04-15
The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum–classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie–Weiss magnet, including N≫1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrix D{sup -hat} (t). Its off-diagonal blocks in a basis selected by the spin–pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final state D{sup -hat} (t{sub f}) that involves correlations between the system and the indications of the pointer, thus ensuring registration. Although D{sup -hat} (t{sub f}) has the form expected for ideal measurements, it only describes a large set of
Quantum measurements without Schroedinger cat states
International Nuclear Information System (INIS)
Spehner, D; Haake, F
2007-01-01
We report and give an alternative derivation of some results on a model for a quantum measurement studied in [1]. The measured microscopic system is coupled to the position of a macroscopic pointer, which itself interacts with its environment via its momentum. The entanglement between the system and the pointer produced by their mutual interaction is simultaneous with the decoherence of distinct pointer readings resulting from leakage of information to the environment. After a discussion on the various time scales in the model we calculate the matrix elements of the system-pointer density operator between eigenstates of the measured observable with distinct eigenvalues. In general, the decay with time of these coherences is neither exponential nor gaussian. We determine the decoherence (decay) time in terms of the strength of the system-pointer and pointer-environment couplings. This decoherence time does not depend upon the details of the pointer-bath coupling as soon as it is smaller than the bath correlation time (non-Markov regime). In contrast, in the Markov regime it depends strongly on whether this coupling is Ohmic or super-Ohmic
Quantum measurements without Schroedinger cat states
Energy Technology Data Exchange (ETDEWEB)
Spehner, D [Institut Fourier, 100 rue des Maths, 38402 Saint-Martin d' Heres (France); Haake, F [Fachbereich Physik, Universitaet Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg (Germany)
2007-10-15
We report and give an alternative derivation of some results on a model for a quantum measurement studied in [1]. The measured microscopic system is coupled to the position of a macroscopic pointer, which itself interacts with its environment via its momentum. The entanglement between the system and the pointer produced by their mutual interaction is simultaneous with the decoherence of distinct pointer readings resulting from leakage of information to the environment. After a discussion on the various time scales in the model we calculate the matrix elements of the system-pointer density operator between eigenstates of the measured observable with distinct eigenvalues. In general, the decay with time of these coherences is neither exponential nor gaussian. We determine the decoherence (decay) time in terms of the strength of the system-pointer and pointer-environment couplings. This decoherence time does not depend upon the details of the pointer-bath coupling as soon as it is smaller than the bath correlation time (non-Markov regime). In contrast, in the Markov regime it depends strongly on whether this coupling is Ohmic or super-Ohmic.
A symmetric geometric measure and the dynamics of quantum discord
International Nuclear Information System (INIS)
Jiang Feng-Jian; Shi Ming-Jun; Lü Hai-Jiang; Yan Xin-Hu
2013-01-01
A symmetric measure of quantum correlation based on the Hilbert—Schmidt distance is presented in this paper. For two-qubit states, we considerably simplify the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically. (general)
Quantum reversibility is relative, or does a quantum measurement reset initial conditions?
Zurek, Wojciech H
2018-07-13
I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer's retention of the information about the measurement outcome. By contrast-even though quantum dynamics is unitary, hence, reversible-reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss-rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer's (branch of) the Universe. Nevertheless, I also show that the observer's friend-an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result-can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).
Sharif, Puya; Heydari, Hoshang
We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by an n-player generalization trough the quantum minority games, and finishing with a contribution towards an n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as a review suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.
Theory of “Weak Value" and Quantum Mechanical Measurements
Shikano, Yutaka
2012-01-01
Comment: to be published from "Measurements in Quantum Mechanics", edited by M. R. Pahlavani (InTech, 2012) Chapter 4 page 75. Yutaka Shikano (2012). ISBN: 978-953-51-0058-4 Available from: http://www.intechopen.com/articles/show/title/theory-of-weak-value-and-quantum-mechanical-measurement
Toward quantum-limited position measurements using optically levitated microspheres
International Nuclear Information System (INIS)
Libbrecht, Kenneth G.; Black, Eric D.
2004-01-01
We propose the use of optically levitated microspheres as test masses in experiments aimed at reaching and potentially exceeding the standard quantum limit for position measurements. Optically levitated microspheres have low mass and are essentially free of suspension thermal noise, making them well suited for experimentally testing our understanding of quantum-limited measurements
Toward quantum-limited position measurements using optically levitated microspheres
Energy Technology Data Exchange (ETDEWEB)
Libbrecht, Kenneth G.; Black, Eric D
2004-01-26
We propose the use of optically levitated microspheres as test masses in experiments aimed at reaching and potentially exceeding the standard quantum limit for position measurements. Optically levitated microspheres have low mass and are essentially free of suspension thermal noise, making them well suited for experimentally testing our understanding of quantum-limited measurements.
Information-theoretic outlook of the quantum dissipation problem
International Nuclear Information System (INIS)
Kowalski, A.M.; Plastino, A.; Proto, A.N.
1992-08-01
The interaction between two harmonic oscillators, a classical and a quantum one, coupled through a linear term, is analyzed by recourse to the generalized Ehrenfest theorem. The model is able to mimic dissipating behaviour for the quantum oscillator without violation of any quantum rule. (author). 13 refs, 5 figs
Quantum trajectories in complex space: One-dimensional stationary scattering problems
International Nuclear Information System (INIS)
Chou, C.-C.; Wyatt, Robert E.
2008-01-01
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems
Demonstration of measurement-only blind quantum computing
International Nuclear Information System (INIS)
Greganti, Chiara; Roehsner, Marie-Christine; Barz, Stefanie; Walther, Philip; Morimae, Tomoyuki
2016-01-01
Blind quantum computing allows for secure cloud networks of quasi-classical clients and a fully fledged quantum server. Recently, a new protocol has been proposed, which requires a client to perform only measurements. We demonstrate a proof-of-principle implementation of this measurement-only blind quantum computing, exploiting a photonic setup to generate four-qubit cluster states for computation and verification. Feasible technological requirements for the client and the device-independent blindness make this scheme very applicable for future secure quantum networks. (paper)
Demonstration of measurement-only blind quantum computing
Greganti, Chiara; Roehsner, Marie-Christine; Barz, Stefanie; Morimae, Tomoyuki; Walther, Philip
2016-01-01
Blind quantum computing allows for secure cloud networks of quasi-classical clients and a fully fledged quantum server. Recently, a new protocol has been proposed, which requires a client to perform only measurements. We demonstrate a proof-of-principle implementation of this measurement-only blind quantum computing, exploiting a photonic setup to generate four-qubit cluster states for computation and verification. Feasible technological requirements for the client and the device-independent blindness make this scheme very applicable for future secure quantum networks.
Energy Technology Data Exchange (ETDEWEB)
Korsch, Hans Juergen
2013-07-01
This book mediates the fundamental terms and methods, which are necessary for an understanding of quantum mechanics. It shows, how mathematics can contribute to the understanding of quantum mechanics. The presented quantum-mechanical problems aim at the illustration and exercise of the most important mathematical methods. Because of the clear and understandable presentation and the numerous completely calculated examples and problems this book is suited for the self-study, for the accompanying of courses on quantum physics, for the accomplishment of exercise problems, and for the preparation on examinations.
Adaptive phase measurements in linear optical quantum computation
International Nuclear Information System (INIS)
Ralph, T C; Lund, A P; Wiseman, H M
2005-01-01
Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state α vertical bar 0>+β vertical bar 1> can be prepared deterministically
Measurement-only topological quantum computation without forced measurements
International Nuclear Information System (INIS)
Zheng, Huaixiu; Dua, Arpit; Jiang, Liang
2016-01-01
We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501) where the braiding operation is shown to be equivalent to a series of topological charge ‘forced measurements’ of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons. (paper)
Weak Measurement and Quantum Smoothing of a Superconducting Qubit
Tan, Dian
In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.
Towards minimal resources of measurement-based quantum computation
International Nuclear Information System (INIS)
Perdrix, Simon
2007-01-01
We improve the upper bound on the minimal resources required for measurement-only quantum computation (M A Nielsen 2003 Phys. Rev. A 308 96-100; D W Leung 2004 Int. J. Quantum Inform. 2 33; S Perdrix 2005 Int. J. Quantum Inform. 3 219-23). Minimizing the resources required for this model is a key issue for experimental realization of a quantum computer based on projective measurements. This new upper bound also allows one to reply in the negative to the open question presented by Perdrix (2004 Proc. Quantum Communication Measurement and Computing) about the existence of a trade-off between observable and ancillary qubits in measurement-only QC
Einstein-Podolsky-Rosen paradox and measurement of quantum system
Kladko, Konstantin
1999-01-01
Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.
Effect of measurement on the quantum kicked reactor
Energy Technology Data Exchange (ETDEWEB)
Sarkar, S; Satchell, J S
1987-07-15
The detailed time-dependent behaviour of the kinetic energy of the quantum kicked rotator is found for both destructive and nondestructive measurement models. This represents a full measurement analysis of a nonlinear dynamical system which shows chaos classically.
Measuring Problem Solving Skills in "Portal 2"
Shute, Valerie J.; Wang, Lubin
2013-01-01
This paper examines possible improvement to problem solving skills as a function of playing the video game "Portal 2." Stealth assessment is used in the game to evaluate students' problem solving abilities--specifically basic and flexible rule application. The stealth assessment measures will be validated against commonly accepted…
Quantum nondemolition measurement saturates fidelity trade-off
International Nuclear Information System (INIS)
Mista, L.; Filip, R.
2005-01-01
Full text: A general quantum measurement on an unknown quantum state enables us to estimate what the state originally was. Simultaneously, the measurement has a destructive effect on a measured quantum state which is reflected by the decrease of the output fidelity. We show for any d-level system that quantum non-demolition measurement controlled by a suitably prepared ancilla is a measurement in which the decrease of the output fidelity is minimal. The ratio between the estimation fidelity and the output fidelity can be continuously controlled by the preparation of the ancilla. Different measurement strategies on the ancilla to gain maximum estimation fidelity are analyzed. A feasible scheme of such a measurement for atomic and optical 2-level systems based on basic controlled-NOT gate is discussed. (author)
Measurement and Quantum State Transfer in Superconducting Qubits
Mlinar, Eric
The potential of superconducting qubits as the medium for a scalable quantum computer has motivated the pursuit of improved interactions within this system. Two challenges for the field of superconducting qubits are measurement fidelity, to accurately determine the state of the qubit, and the efficient transfer of quantum states. In measurement, the current state-of-the-art method employs dispersive readout, by coupling the qubit to a cavity and reading the resulting shift in cavity frequency to infer the qubit's state; however, this is vulnerable to Purcell relaxation, as well as being modeled off a simplified two-level abstraction of the qubit. In state transfer, the existing proposal for moving quantum states is mostly untested against non-idealities that will likely be present in an experiment. In this dissertation, we examine three problems within these two areas. We first describe a new scheme for fast and high-fidelity dispersive measurement specifically designed to circumvent the Purcell Effect. To do this, the qubit-resonator interaction is turned on only when the resonator is decoupled from the environment; then, after the resonator state has shifted enough to infer the qubit state, the qubit-resonator interaction is turned off before the resonator and environment are recoupled. We also show that the effectiveness of this "Catch-Disperse-Release'' procedure partly originates from quadrature squeezing of the resonator state induced by the Jaynes-Cummings nonlinearity. The Catch-Disperse-Release measurement scheme treats the qubit as a two-level system, which is a common simplification used in theoretical works. However, the most promising physical candidate for a superconducting qubit, the transmon, is a multi-level system. In the second work, we examine the effects of including the higher energy levels of the transmon. Specifically, we expand the eigenstate picture developed in the first work to encompass multiple qubit levels, and examine the resulting
Fidelity induced distance measures for quantum states
International Nuclear Information System (INIS)
Ma Zhihao; Zhang Fulin; Chen Jingling
2009-01-01
Fidelity plays an important role in quantum information theory. In this Letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case. The metric character is also presented for the qudit (i.e., d-dimensional system) case. The CPT contractive property and joint convex property of the metric are also studied.
Bass, Gideon; Tomlin, Casey; Kumar, Vaibhaw; Rihaczek, Pete; Dulny, Joseph, III
2018-04-01
NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.
The preparation problem in nonlinear extensions of quantum theory
Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.
2012-01-01
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...
Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases.
Pezzè, Luca; Ciampini, Mario A; Spagnolo, Nicolò; Humphreys, Peter C; Datta, Animesh; Walmsley, Ian A; Barbieri, Marco; Sciarrino, Fabio; Smerzi, Augusto
2017-09-29
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.
Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases
Pezzè, Luca; Ciampini, Mario A.; Spagnolo, Nicolò; Humphreys, Peter C.; Datta, Animesh; Walmsley, Ian A.; Barbieri, Marco; Sciarrino, Fabio; Smerzi, Augusto
2017-09-01
A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.
Measurement-based local quantum filters and their ability to ...
Indian Academy of Sciences (India)
Debmalya Das
2017-05-30
May 30, 2017 ... Entanglement; local filters; quantum measurement. PACS No. 03.65 ... ties [4,5], it also plays a key role in quantum computing where it is ... Furthermore, we pro- vide an ..... Corresponding to each of these vectors, we can con-.
Muon 2 measurements and non-commutative geometry of quantum ...
Indian Academy of Sciences (India)
Abstract. We discuss a completely quantum mechanical treatment of the measurement of the anomalous magnetic moment of the muon. A beam of muons move in a strong uniform magnetic field and a weak focusing electrostatic field. Errors in the classical beam analysis are exposed. In the Dirac quantum beam analysis, ...
A review on economic emission dispatch problems using quantum computational intelligence
Mahdi, Fahad Parvez; Vasant, Pandian; Kallimani, Vish; Abdullah-Al-Wadud, M.
2016-11-01
Economic emission dispatch (EED) problems are one of the most crucial problems in power systems. Growing energy demand, limitation of natural resources and global warming make this topic into the center of discussion and research. This paper reviews the use of Quantum Computational Intelligence (QCI) in solving Economic Emission Dispatch problems. QCI techniques like Quantum Genetic Algorithm (QGA) and Quantum Particle Swarm Optimization (QPSO) algorithm are discussed here. This paper will encourage the researcher to use more QCI based algorithm to get better optimal result for solving EED problems.
Programming and Tuning a Quantum Annealing Device to Solve Real World Problems
Perdomo-Ortiz, Alejandro; O'Gorman, Bryan; Fluegemann, Joseph; Smelyanskiy, Vadim
2015-03-01
Solving real-world applications with quantum algorithms requires overcoming several challenges, ranging from translating the computational problem at hand to the quantum-machine language to tuning parameters of the quantum algorithm that have a significant impact on the performance of the device. In this talk, we discuss these challenges, strategies developed to enhance performance, and also a more efficient implementation of several applications. Although we will focus on applications of interest to NASA's Quantum Artificial Intelligence Laboratory, the methods and concepts presented here apply to a broader family of hard discrete optimization problems, including those that occur in many machine-learning algorithms.
International Nuclear Information System (INIS)
Yu Watanabe; Masahito Ueda
2012-01-01
Full text: When we try to obtain information about a quantum system, we need to perform measurement on the system. The measurement process causes unavoidable state change. Heisenberg discussed a thought experiment of the position measurement of a particle by using a gamma-ray microscope, and found a trade-off relation between the error of the measured position and the disturbance in the momentum caused by the measurement process. The trade-off relation epitomizes the complementarity in quantum measurements: we cannot perform a measurement of an observable without causing disturbance in its canonically conjugate observable. However, at the time Heisenberg found the complementarity, quantum measurement theory was not established yet, and Kennard and Robertson's inequality erroneously interpreted as a mathematical formulation of the complementarity. Kennard and Robertson's inequality actually implies the indeterminacy of the quantum state: non-commuting observables cannot have definite values simultaneously. However, Kennard and Robertson's inequality reflects the inherent nature of a quantum state alone, and does not concern any trade-off relation between the error and disturbance in the measurement process. In this talk, we report a resolution to the complementarity in quantum measurements. First, we find that it is necessary to involve the estimation process from the outcome of the measurement for quantifying the error and disturbance in the quantum measurement. We clarify the implicitly involved estimation process in Heisenberg's gamma-ray microscope and other measurement schemes, and formulate the error and disturbance for an arbitrary quantum measurement by using quantum estimation theory. The error and disturbance are defined in terms of the Fisher information, which gives the upper bound of the accuracy of the estimation. Second, we obtain uncertainty relations between the measurement errors of two observables [1], and between the error and disturbance in the
Some problems of quantum cosmology and dark matter physics
Wang, Jin
The quantum cosmology is studied of the string universe obtained by embedding the Robertson-Walker metric in the nonlinear sigma model. It was found that initially the universe exists in a series of metastable bound states with the scale factor taking discrete values. Then it tunnels through a barrier and comes out in an inflationary state. This tunneling (or evolution in imaginary time) also has the effect of heating up the matter field so that we have a condition of chaotic inflation. The asymptotic solutions agree with those obtained from the classical Einstein equations. Quantum cosmology was considered of a 4-D universe using the effective action of superstrings. Both Hartle-Hawking and Vilenkin boundary conditions were applied to the solution of Wheeler-DeWitt equation. Under certain conditions (fermions added) the universe was found to tunnel through to the Lorentzian regime from the Euclidean regime and time is dynamically generated. Chudnovsky and Vilenkin's idea was applied to possible existence of cosmic strings in the Sun. Stellar evolution with cosmic strings at solar age gives a radius and luminosity of the star which are in contradiction with observation. The astrophysical bound was studied on the change of gravitational constant with time. It was found that (G/G) less than 10-12yr-1 is the condition that has to be satisfied in order not to cause the conflict with observation. The effect was studied of axions on the steller evolution of a 10 solar mass star model. If the axion mass is larger than .1 ev the star's age is significantly different at late stages, compared to the star without axions. It is argued that if cosmions (or WIMPS) solve the solar neutrino problem, then they must also play an important role in the evolution of low mass star main sequence stars. If they do so, then a simple (long mean free path) model for the interaction of cosmions with baryons leads to changes in the structure of the nuclear-burning core which may in principle
Quantum trajectories and measurements in continuous time. The diffusive case
International Nuclear Information System (INIS)
Barchielli, Alberto; Gregoratti, Matteo
2009-01-01
This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schroedinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow's triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in
Internal Performance Measurement Systems: Problems and Solutions
DEFF Research Database (Denmark)
Jakobsen, Morten; Mitchell, Falconer; Nørreklit, Hanne
2010-01-01
This article pursues two aims: to identify problems and dangers related to the operational use of internal performance measurement systems of the Balanced Scorecard (BSC) type and to provide some guidance on how performance measurement systems may be designed to overcome these problems....... The analysis uses and extends N rreklit's (2000) critique of the BSC by applying the concepts developed therein to contemporary research on the BSC and to the development of practice in performance measurement. The analysis is of relevance for many companies in the Asia-Pacific area as an increasing numbers...
International Nuclear Information System (INIS)
Loock, Peter van; Nemoto, Kae; Munro, William J.; Raynal, Philippe; Luetkenhaus, Norbert
2006-01-01
We discuss the problem of implementing generalized measurements [positive operator-valued measures (POVMs)] with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states
International Nuclear Information System (INIS)
Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H F
2013-01-01
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state. (paper)
Blind quantum computation protocol in which Alice only makes measurements
Morimae, Tomoyuki; Fujii, Keisuke
2013-05-01
Blind quantum computation is a new secure quantum computing protocol which enables Alice (who does not have sufficient quantum technology) to delegate her quantum computation to Bob (who has a full-fledged quantum computer) in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experimental setups, such as optical systems, the measurement of a state is much easier than the generation of a single-qubit state. Therefore our protocols ease Alice's burden. Furthermore, the security of our protocol is based on the no-signaling principle, which is more fundamental than quantum physics. Finally, our protocols are device independent in the sense that Alice does not need to trust her measurement device in order to guarantee the security.
Fast reconstruction of high-qubit-number quantum states via low-rate measurements
Li, K.; Zhang, J.; Cong, S.
2017-07-01
Due to the exponential complexity of the resources required by quantum state tomography (QST), people are interested in approaches towards identifying quantum states which require less effort and time. In this paper, we provide a tailored and efficient method for reconstructing mixed quantum states up to 12 (or even more) qubits from an incomplete set of observables subject to noises. Our method is applicable to any pure or nearly pure state ρ and can be extended to many states of interest in quantum information processing, such as a multiparticle entangled W state, Greenberger-Horne-Zeilinger states, and cluster states that are matrix product operators of low dimensions. The method applies the quantum density matrix constraints to a quantum compressive sensing optimization problem and exploits a modified quantum alternating direction multiplier method (quantum-ADMM) to accelerate the convergence. Our algorithm takes 8 ,35 , and 226 seconds, respectively, to reconstruct superposition state density matrices of 10 ,11 ,and12 qubits with acceptable fidelity using less than 1 % of measurements of expectation. To our knowledge it is the fastest realization that people can achieve using a normal desktop. We further discuss applications of this method using experimental data of mixed states obtained in an ion trap experiment of up to 8 qubits.
Stability of continuous-time quantum filters with measurement imperfections
Amini, H.; Pellegrini, C.; Rouchon, P.
2014-07-01
The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes and that takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems and where the measurement imperfections are modelled by a left stochastic matrix.
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Semiclassical expansion of quantum characteristics for many-body potential scattering problem
International Nuclear Information System (INIS)
Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.
2007-01-01
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
A new quantum inspired chaotic artificial bee colony algorithm for optimal power flow problem
International Nuclear Information System (INIS)
Yuan, Xiaohui; Wang, Pengtao; Yuan, Yanbin; Huang, Yuehua; Zhang, Xiaopan
2015-01-01
Highlights: • Quantum theory is introduced to artificial bee colony algorithm (ABC) to increase population diversity. • A chaotic local search operator is used to enhance local search ability of ABC. • Quantum inspired chaotic ABC method (QCABC) is proposed to solve optimal power flow. • The feasibility and effectiveness of the proposed QCABC is verified by examples. - Abstract: This paper proposes a new artificial bee colony algorithm with quantum theory and the chaotic local search strategy (QCABC), and uses it to solve the optimal power flow (OPF) problem. Under the quantum computing theory, the QCABC algorithm encodes each individual with quantum bits to form a corresponding quantum bit string. By determining each quantum bits value, we can get the value of the individual. After the scout bee stage of the artificial bee colony algorithm, we begin the chaotic local search in the vicinity of the best individual found so far. Finally, the quantum rotation gate is used to process each quantum bit so that all individuals can update toward the direction of the best individual. The QCABC algorithm is carried out to deal with the OPF problem in the IEEE 30-bus and IEEE 118-bus standard test systems. The results of the QCABC algorithm are compared with other algorithms (artificial bee colony algorithm, genetic algorithm, particle swarm optimization algorithm). The comparison shows that the QCABC algorithm can effectively solve the OPF problem and it can get the better optimal results than those of other algorithms
Stochastic dynamics approach to tunneling problems in quantum mechanics
International Nuclear Information System (INIS)
Jona-Lasinio, G.; Martinelli, F.; Scoppola, E.
1981-01-01
The authors' main purpose is to give a general procedure to estimate the splittings of the ground state, due to tunneling, of finite one-dimensional quantum systems in the semiclassical limit h/2π→0. (Auth.)
Exceptional points and quantum correlations in precise measurements
International Nuclear Information System (INIS)
Thilagam, A
2012-01-01
We examine the physical manifestations of exceptional points and passage times in a two-level system which is subjected to quantum measurements and which admits a non-Hermitian description. Using an effective Hamiltonian acting in the two-dimensional space spanned by the evolving initial and final states, the effects of highly precise quantum measurements in which the monitoring device interferes significantly with the evolution dynamics of the monitored two-level system is analyzed. The dynamics of a multipartite system consisting of the two-level system, a source of external potential and the measurement device is examined using correlation measures such as entanglement and non-classical quantum correlations. Results show that the quantum correlations between the monitored (monitoring) systems is considerably decreased (increased) as the measurement precision nears the exceptional point, at which the passage time is half of the measurement duration. The results indicate that the underlying mechanism by which the non-classical correlations of quantum systems are transferred from one subsystem to another may be better revealed via use of geometric approaches. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)
Quantum Measurement Theory in Gravitational-Wave Detectors
Directory of Open Access Journals (Sweden)
Stefan L. Danilishin
2012-04-01
Full Text Available The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
Quantum Measurement Theory in Gravitational-Wave Detectors.
Danilishin, Stefan L; Khalili, Farid Ya
2012-01-01
The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
On the Quantum Inverse problem for the continuous Heisenberg spin chain with axial anisotropy
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Chanda, P.K.
1986-06-01
We have considered the Quantum Inverse problem for the continuous form of Heisenberg spin chain with anisotropy. The form of quantum R-matrix, the commutation rules for the scattering data, and the explicit structure of the excitation spectrum are obtained. (author)
Value preserving quantum measurements: impossibility theorems and lower bounds for the distortion
International Nuclear Information System (INIS)
Ghirardi, G.C.; Trieste Univ.; Rimini, A.; Weber, T.
1982-11-01
Extending previous works on the subject, we consider the problem of the limitations to ideal quantum measurements arising from the presence of additive conservation laws. We derive impossibility theorems and lower bounds for the deviations from the ideal schemes, with particular reference to the distorting case. (author)
Self-guaranteed measurement-based quantum computation
Hayashi, Masahito; Hajdušek, Michal
2018-05-01
In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted for correlations between several subsystems. If we do not trust the measurement basis or the prepared entangled state, we do need to be worried about such uncertainties. To this end, we propose a self-guaranteed protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis or entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client, who drives the computation by single-qubit measurements. Applying self-testing procedures, we are able to verify the initial resource as well as the operation of the quantum devices and hence the computation itself. The overhead of our protocol scales with the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.
International Nuclear Information System (INIS)
Garon, Ariane
2014-01-01
Since the foundations of quantum physics have been laid, our knowledge of it never ceased to grow and this field of science naturally split into diverse specialized branches. The first part of this thesis focuses on a problem which concerns all branches of quantum physics, which is the visualization of quantum systems. The non-intuitive aspect of quantum physics justifies a shared desire to visualize quantum systems. In the present work, we develop a method to visualize any operators in these systems, including in particular state operators (density matrices), Hamiltonians and propagators. The method, referred to as DROPS (Discrete Representation of spin OPeratorS), is based on a generalization of Wigner representations, presented in this document. The resulting visualization of an operator A is called its DROPS representation or visualization. We demonstrate its intuitive character by illustrating a series of concepts in nuclear magnetic resonance (NMR) spectroscopy for systems consisting of two spin-1/2 particles. The second part of this thesis is concerned with a problem of optimal control which finds applications in the fields of NMR spectroscopy, medical imagery and quantum computing, to cite a few. The problem of creating a propagator in the shortest amount of time is considered, and the results are extended to solve the closely related problem of creating rotations in the smallest amount of time. The approach used here differs from the previous results on the subject by solving the problem using the Pontryagin's maximum principle and by its detailed consideration of singular controls and trajectories.
Measuring the effective phonon density of states of a quantum dot in cavity quantum electrodynamics
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Nielsen, Per Kær; Kreiner-Møller, Asger
2013-01-01
We employ detuning-dependent decay-rate measurements of a quantum dot in a photonic-crystal cavity to study the influence of phonon dephasing in a solid-state quantum-electrodynamics experiment. The experimental data agree with a microscopic non-Markovian model accounting for dephasing from...... longitudinal acoustic phonons, and the analysis explains the difference between nonresonant cavity feeding in different nanocavities. From the comparison between experiment and theory we extract the effective phonon density of states experienced by the quantum dot in the nanocavity. This quantity determines...
Pressing problems of measurement of ionizing radiations
International Nuclear Information System (INIS)
Fominykh, V.I.; Yudin, M.F.
1993-01-01
The current system for ensuring the unity of measurements in the Russian Federation and countries of the former Soviet Union ensures a high quality of dosimetric, radiometric, and spectrometric measurements in accordance with the recommendations of the Consulative Committee on Standards for Measurements of Ionizing Radiations of the International Bureau of Weights and Measures (IBWM), International Organization on Radiological Units (ICRU), International Commission on Radiological Protection (ICRP), International Organization on Legislative Metrology (IOLM), International Atomic Energy Agency (IAEA), World Health Organization (WHO), etc. Frequent collation of the national primary and secondary standards of Russia with those of IBWM and the leading national laboratories of the world facilitate mutual verification of the measurements of ionizing radiations. The scope of scientific and scientific-technical problems that can be solved by using ionizing radiations has expanded significantly in recent years. In this paper the authors consider some pressing problems of the metrology of ionizing radiations which have arisen as a result of this expansion. These include the need for unity and reliability of measurements involved in radiation protection, the measurement of low doses involving low dose rates, ensuring the unity of measurements when monitoring the radiological security of the population, the need for more uniformity on an international scale regarding the basic physical quantities and their units for characterizing radiation fields, determination of the accuracy of measurement of the radiation dose absorbed by an irradiated tissue or organ, and the development of complex standards for ionizing radiations. 5 refs., 1 tab
Applications of the infinite momentum method to quantum electrodynamics and bound state problem
International Nuclear Information System (INIS)
Brodsky, S.J.
1973-01-01
It is shown that the infinite momentum method is a valid and useful calculational alternative to standard perturbation theory methods. The most exciting future applications may be in bound state problems in quantum electrodynamics
Quantum coherence in the time-resolved Auger measurement
Energy Technology Data Exchange (ETDEWEB)
Smirnova, Olga; Yakovlev, Vladislav S; Scrinzi, Armin
2003-12-19
We present a quantum mechanical model of the attosecond-XUV (extreme ultraviolet) pump and laser probe measurement of an Auger decay [Drescher et al., Nature (London) 419, 803 (2002)10.1038/nature01143] and investigate effects of quantum coherence. The time-dependent Schroedinger equation is solved by numerical integration and in analytic form. We explain the transition from a quasiclassical energy shift of the spectrum to the formation of sidebands and the enhancement of high- and low-energy tails of the Auger spectrum due to quantum coherence between photoionization and Auger decay.
Sturm solutions of the two-centre problem in quantum mechanics
International Nuclear Information System (INIS)
Truskova, N.F.
1984-01-01
Algorithm of computer calculation of the Sturm solutions of the two-body problem in quantum mechanics has been presented for different magnitudes of internuclear distance R and at energies E<0, which correspond to a definite term of the above problem or to a constants. Formulae of transition from spherical quantum numbers to parabolic ones have been presented, and asymptotics of eigen values at R→0 and R→infinity have been obtained. Calculation results are presented in a graphical form
Covariance operator of functional measure in P(φ)2-quantum field theory
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Zhidkov, E.P.
1988-01-01
Functional integration measure in the Euclidean quantum field theory with polynomial interactions of boson fields with zero spin in two-dimensional space-time is investigated. The representation for the kernal of the measure covariance operator is obtained in the form of expansion over the eigenfunctions of some boundary problem for the heat equation. Two cases of the integration domains with different configurations are considered. Some trends and perspectives of employing the functional integration method in quantum field theory are also discussed. 43 refs
Theoretical physics IV. Quantum mechanics with problems in MAPLE
International Nuclear Information System (INIS)
Reinecker, Peter; Schulz, Michael; Schulz, Beatrix M.
2008-01-01
Quantum mechanics 2 is the fourth volume of the new and unique series for theoretical physics with Maple applications. This from basics newly concipated series mediates theoretical physics from contemporary view and in a way referring to a comprehensive lecture experience. Extensively and completely in five consecutively appearing volumes classical mechanics, electrodynamics, quantum mechanics 1 and 2, as well as statistical physics and thermodynamics are presented. Additionally for the elegant and extensive presentation on an each added CP applications for MAPLE trademark are contained, the software, which at more and more university is already applied in the lecture. They allow the experimenting with theory - and facilitate the understanding essentially. The present volume mediates extending, more complex contents of quantum mechanics, which are based on volume III of the series
Some problems in the interpretation of quantum mechanics
International Nuclear Information System (INIS)
Wallace, P.R.
1990-01-01
Recently, a number of books have appeared purporting to explain quantum mechanics to the general public. These books have put considerable emphasis on so-called quantum 'paradoxes', using them to portray the quantum theory as mysterious or 'spooky'. We discuss these 'paradoxes' from a different viewpoint with the aim of demystifying the theory. Emphasis is shifted from an epistemological viewpoint (as exemplified by the 'probability interpretation') to an ontological one (the description of matter by physical fields). Difficulties in reconciling the probability interpretation with relativity are noted, and the importance of phase coherence, which is inadequately treated in the probability interpretation, is emphasised. In the light of such an approach, the 'paradoxes' are resolved. (author)
Solving quantum optimal control problems using Clebsch variables and Lin constraints
Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.
2018-01-01
Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.
Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals
Paraoanu, G. S.
2011-07-01
We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system.
Weak measurements and quantum weak values for NOON states
Rosales-Zárate, L.; Opanchuk, B.; Reid, M. D.
2018-03-01
Quantum weak values arise when the mean outcome of a weak measurement made on certain preselected and postselected quantum systems goes beyond the eigenvalue range for a quantum observable. Here, we propose how to determine quantum weak values for superpositions of states with a macroscopically or mesoscopically distinct mode number, that might be realized as two-mode Bose-Einstein condensate or photonic NOON states. Specifically, we give a model for a weak measurement of the Schwinger spin of a two-mode NOON state, for arbitrary N . The weak measurement arises from a nondestructive measurement of the two-mode occupation number difference, which for atomic NOON states might be realized via phase contrast imaging and the ac Stark effect using an optical meter prepared in a coherent state. The meter-system coupling results in an entangled cat-state. By subsequently evolving the system under the action of a nonlinear Josephson Hamiltonian, we show how postselection leads to quantum weak values, for arbitrary N . Since the weak measurement can be shown to be minimally invasive, the weak values provide a useful strategy for a Leggett-Garg test of N -scopic realism.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2014-11-01
Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Measurement and the mathematical apparatus of quantum physics
International Nuclear Information System (INIS)
Slavnov, D.A.
2007-01-01
A scheme for constructing quantum mechanics in which the Hilbert space and linear operators are not primary elements on the theory is described. Some variant of the algebraic approach is instead considered. The elements of a noncommutative algebra (observables) and functionals in this algebra serve as the primary components of the theory. Such a scheme allows one to use the formalism of the classical (Kolmogorovian) theory of probability, and to reproduce the mathematical formalism of standard quantum mechanics and to specify borders of its applicability. A brief review of necessary data from the theory of algebras and probability theory is given. The manner is described in which the considered mathematical scheme agrees with the theory of quantum measurements and allows one to avoid quantum paradoxes [ru
Direct measurement of nonlinear properties of bipartite quantum states.
Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Paweł; Alves, Carolina Moura; Sergienko, Alexander Vladimir
2005-12-09
Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely, the Renyi entropy, from local measurements on two pairs of polarization-entangled photons. We also introduce a "phase marking" technique which allows the selection of uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of nonlinear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-Clauser-Horne-Shimony-Holt inequalities.
Quantum continual measurements and a posteriori collapse on CCR
International Nuclear Information System (INIS)
Belavkin, V.P.
1992-01-01
A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one. (orig.)
Measurement-device-independent quantum communication with an untrusted source
Xu, Feihu
2015-07-01
Measurement-device-independent quantum key distribution (MDI-QKD) can provide enhanced security compared to traditional QKD, and it constitutes an important framework for a quantum network with an untrusted network server. Still, a key assumption in MDI-QKD is that the sources are trusted. We propose here a MDI quantum network with a single untrusted source. We have derived a complete proof of the unconditional security of MDI-QKD with an untrusted source. Using simulations, we have considered various real-life imperfections in its implementation, and the simulation results show that MDI-QKD with an untrusted source provides a key generation rate that is close to the rate of initial MDI-QKD in the asymptotic setting. Our work proves the feasibility of the realization of a quantum network. The network users need only low-cost modulation devices, and they can share both an expensive detector and a complicated laser provided by an untrusted network server.
Memory-assisted measurement-device-independent quantum key distribution
Panayi, Christiana; Razavi, Mohsen; Ma, Xiongfeng; Lütkenhaus, Norbert
2014-04-01
A protocol with the potential of beating the existing distance records for conventional quantum key distribution (QKD) systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of measurement-device-independent QKD, which only requires optical source equipment at the user's end. For certain memories with short access times, our scheme allows a higher repetition rate than that of quantum repeaters with single-mode memories, thereby requiring lower coherence times. By accounting for various sources of nonideality, such as memory decoherence, dark counts, misalignment errors, and background noise, as well as timing issues with memories, we develop a mathematical framework within which we can compare QKD systems with and without memories. In particular, we show that with the state-of-the-art technology for quantum memories, it is potentially possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations.
Quantum measurement and real-time feedback with a spin-register in diamond
Blok, M.S.
2015-01-01
Gaining precise control over quantum systems is crucial for applications in quantum information processing and quantum sensing and to perform experimental tests of quantum mechanics. The experiments presented in this thesis implement quantum measurements and real-time feedback protocols that can
Quantum limits to center-of-mass measurements
International Nuclear Information System (INIS)
Vaughan, Timothy; Drummond, Peter; Leuchs, Gerd
2007-01-01
We discuss the issue of measuring the mean position (center of mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultralow temperatures, and discuss this limit in the context of both photons and ultracold atoms. In the case of non-interacting harmonically trapped fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a 1/N scaling in the position standard deviation--as opposed to a 1/√(N) scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center of mass. This macroscopic quantum effect cannot be readily observed for noninteracting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles
Quantum Bayesian rule for weak measurements of qubits in superconducting circuit QED
International Nuclear Information System (INIS)
Wang, Peiyue; Qin, Lupei; Li, Xin-Qi
2014-01-01
Compared with the quantum trajectory equation (QTE), the quantum Bayesian approach has the advantage of being more efficient to infer a quantum state under monitoring, based on the integrated output of measurements. For weak measurement of qubits in circuit quantum electrodynamics (cQED), properly accounting for the measurement backaction effects within the Bayesian framework is an important problem of current interest. Elegant work towards this task was carried out by Korotkov in ‘bad-cavity’ and weak-response limits (Korotkov 2011 Quantum Bayesian approach to circuit QED measurement (arXiv:1111.4016)). In the present work, based on insights from the cavity-field states (dynamics) and the help of an effective QTE, we generalize the results of Korotkov to more general system parameters. The obtained Bayesian rule is in full agreement with Korotkov's result in limiting cases and as well holds satisfactory accuracy in non-limiting cases in comparison with the QTE simulations. We expect the proposed Bayesian rule to be useful for future cQED measurement and control experiments. (paper)
An approach using quantum PBIL to solve the traveling salesman problem
International Nuclear Information System (INIS)
Silva, Marcio Henrique; Schirru, Roberto
2011-01-01
Quantum inspired evolutionary algorithms are optimization tools based in artificial intelligence developed to simulate the quantum processing in classical computers viewing that there are not quantum computers available nowadays. In this work is introduced one of these tools, which adds quantum concepts such as the linear superposition of states and the qubit representation to standard PBIL named Quantum PBIL. Here we use Quantum PBIL to solve a well-known NPHard benchmark, the Traveling salesman problem. The objective is to find the shorter path made by a traveler linking all the available cities visiting each one only once and returning to the starter one at the final of his journey. As the main purpose of this work is employ the algorithm to solve the nuclear reload optimization in the future, and according to the similarities that both problems share, TSP is a good challenge for Quantum PBIL. The results have shown that the algorithm is able to obtain good performance when applied on this problem. It is also fast and has a great capacity to find good solutions when compared to other versions of PBIL found in literature despite of its stagnation of bits tendency can easily lead it to local minimums. (author)
An approach using quantum PBIL to solve the traveling salesman problem
Energy Technology Data Exchange (ETDEWEB)
Silva, Marcio Henrique; Schirru, Roberto, E-mail: marciohenrique@lmp.ufrj.br, E-mail: schirru@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (PEN/COPPE), Rio de Janeiro, RJ (Brazil)
2011-07-01
Quantum inspired evolutionary algorithms are optimization tools based in artificial intelligence developed to simulate the quantum processing in classical computers viewing that there are not quantum computers available nowadays. In this work is introduced one of these tools, which adds quantum concepts such as the linear superposition of states and the qubit representation to standard PBIL named Quantum PBIL. Here we use Quantum PBIL to solve a well-known NPHard benchmark, the Traveling salesman problem. The objective is to find the shorter path made by a traveler linking all the available cities visiting each one only once and returning to the starter one at the final of his journey. As the main purpose of this work is employ the algorithm to solve the nuclear reload optimization in the future, and according to the similarities that both problems share, TSP is a good challenge for Quantum PBIL. The results have shown that the algorithm is able to obtain good performance when applied on this problem. It is also fast and has a great capacity to find good solutions when compared to other versions of PBIL found in literature despite of its stagnation of bits tendency can easily lead it to local minimums. (author)
Optimal and secure measurement protocols for quantum sensor networks
Eldredge, Zachary; Foss-Feig, Michael; Gross, Jonathan A.; Rolston, S. L.; Gorshkov, Alexey V.
2018-04-01
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
Quantum measurement and quantum gravity: many-worlds or collapse of the wavefunction?
International Nuclear Information System (INIS)
Singh, T P
2009-01-01
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wavefunction collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes nonlinear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this nonlinear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a nonlinear Schroedinger equation, which can explain collapse of the wavefunction. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model.
On the two-body problem in quantum mechanics
International Nuclear Information System (INIS)
Micu, L.
2008-01-01
Following the representation of a two-body system in classical mechanics, we build up a quantum picture which is free of spurious effects and retains the intrinsic features of the internal bodies. In the coordinate space the system is represented by the real particles, individually bound to a center of forces which in a certain limit coincides with the center of mass and the wave function writes as product of the individual wave functions with correlated arguments. (author)
Quantum Secure Dialogue with Quantum Encryption
International Nuclear Information System (INIS)
Ye Tian-Yu
2014-01-01
How to solve the information leakage problem has become the research focus of quantum dialogue. In this paper, in order to overcome the information leakage problem in quantum dialogue, a novel approach for sharing the initial quantum state privately between communicators, i.e., quantum encryption sharing, is proposed by utilizing the idea of quantum encryption. The proposed protocol uses EPR pairs as the private quantum key to encrypt and decrypt the traveling photons, which can be repeatedly used after rotation. Due to quantum encryption sharing, the public announcement on the state of the initial quantum state is omitted, thus the information leakage problem is overcome. The information-theoretical efficiency of the proposed protocol is nearly 100%, much higher than previous information leakage resistant quantum dialogue protocols. Moreover, the proposed protocol only needs single-photon measurements and nearly uses single photons as quantum resource so that it is convenient to implement in practice. (general)
High-Efficiency Quantum Interrogation Measurements via the Quantum Zeno Effect
International Nuclear Information System (INIS)
Kwiat, P. G.; White, A. G.; Mitchell, J. R.; Nairz, O.; Weihs, G.; Weinfurter, H.; Zeilinger, A.
1999-01-01
The phenomenon of quantum interrogation allows one to optically detect the presence of an absorbing object, without the measuring light interacting with it. In an application of the quantum Zeno effect, the object inhibits the otherwise coherent evolution of the light, such that the probability that an interrogating photon is absorbed can in principle be arbitrarily small. We have implemented this technique, achieving efficiencies of up to 73% , and consequently exceeding the 50% theoretical maximum of the original ''interaction-free'' measurement proposal. We have also predicted and experimentally verified a previously unsuspected dependence on loss. (c) 1999 The American Physical Society
Probing 2D black phosphorus by quantum capacitance measurements
International Nuclear Information System (INIS)
Kuiri, Manabendra; Kumar, Chandan; Chakraborty, Biswanath; Gupta, Satyendra N; Naik, Mit H; Jain, Manish; Sood, A K; Das, Anindya
2015-01-01
Two-dimensional materials and their heterostructures have emerged as a new class of materials, not only for fundamental physics but also for electronic and optoelectronic applications. Black phosphorus (BP) is a relatively new addition to this class of materials. Its strong in-plane anisotropy makes BP a unique material for making conceptually new types of electronic devices. However, the global density of states (DOS) of BP in device geometry has not been measured experimentally. Here, we report the quantum capacitance measurements together with the conductance measurements on an hBN-protected few-layer BP (∼six layers) in a dual-gated field effect transistor (FET) geometry. The measured DOS from our quantum capacitance is compared with density functional theory (DFT). Our results reveal that the transport gap for quantum capacitance is smaller than that in conductance measurements due to the presence of localized states near the band edge. The presence of localized states is confirmed by the variable range hopping seen in our temperature dependence conductivity. A large asymmetry is observed between the electron and hole side. This asymmetric nature is attributed to the anisotropic band dispersion of BP. Our measurements establish the uniqueness of quantum capacitance in probing the localized states near the band edge, hitherto not seen in conductance measurements. (paper)
Galitski, Victor; Kogan, Vladimir; Galitski, Victor Jr
2013-01-01
A series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial task and its deep understanding can only be achieved through working out real-life problems and examples. It is notoriously difficult to come up with new quantum-mechanical problems that would be solvable with a pencil and paper, and within a finite amount of time. This book remarkably presents some 700+ original problems in quantum mechanics together with detailed solutions covering nearly 1000 pages on all aspects of quantum science. The material is largely new to the English-speaking audience. The problems have been collect...
Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.
2018-01-01
Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to predict binding specificity. Using simplified datasets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified datasets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems. PMID:29652405
Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.
2018-03-01
Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to classify and rank binding affinities. Using simplified data sets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified data sets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems.
Energy Technology Data Exchange (ETDEWEB)
Spoerl, Andreas
2008-06-05
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
Estimation of atomic interaction parameters by quantum measurements
DEFF Research Database (Denmark)
Kiilerich, Alexander Holm; Mølmer, Klaus
Quantum systems, ranging from atomic systems to field modes and mechanical devices are useful precision probes for a variety of physical properties and phenomena. Measurements by which we extract information about the evolution of single quantum systems yield random results and cause a back actio...... strategies, we address the Fisher information and the Cramér-Rao sensitivity bound. We investigate monitoring by photon counting, homodyne detection and frequent projective measurements respectively, and exemplify by Rabi frequency estimation in a driven two-level system....
Quantum learning of classical stochastic processes: The completely positive realization problem
Monràs, Alex; Winter, Andreas
2016-01-01
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine
Quantum learning of classical stochastic processes: The completely positive realization problem
Energy Technology Data Exchange (ETDEWEB)
Monràs, Alex [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Winter, Andreas [Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); ICREA—Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys, 23, 08010 Barcelona (Spain)
2016-01-15
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine
Quantum learning of classical stochastic processes: The completely positive realization problem
International Nuclear Information System (INIS)
Monràs, Alex; Winter, Andreas
2016-01-01
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine
International Nuclear Information System (INIS)
Ji, Un Cig; Obata, Nobuaki
2010-01-01
The implementation problem for the canonical commutation relation is reduced to a system of differential equations for Fock space operators containing new type of derivatives. We solve these differential equations systematically by means of quantum white noise calculus, and obtain the solution to the implementation problem.
Quantum description of microscopic and macroscopic systems: Old problems and recent investigations
International Nuclear Information System (INIS)
Ghirardi, G.C.
1986-04-01
We review some open problems and some proposed solutions which are encountered in the quantum description of the microscopic systems, of the macroscopic ones, and of the interactions between these two types of objects. We describe a recent attempt allowing a unified description of all phenomena, reproducing the quantum mechanical situation for microscopic systems and inducing in a completely consistent way the classical behaviour of macro object and the phenomena of wave packet reduction in the system-apparatus interaction. (author)
On the problem of quantum control in infinite dimensions
Mendes, R. Vilela; Man'ko, Vladimir I.
2010-01-01
In the framework of bilinear control of the Schr\\"odinger equation with bounded control operators, it has been proved that the reachable set has a dense complemement in ${\\cal S}\\cap {\\cal H}^{2}$. Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this...
Foundations and measures of quantum non-Markovianity
International Nuclear Information System (INIS)
Breuer, Heinz-Peter
2012-01-01
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behaviour. Here, we review recent ideas developing a general mathematical definition for non-Markovianity in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems, which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system–environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system. (topical review)
Li, Fei; Zhao, Wei; Guo, Ying
2018-01-01
Continuous-variable (CV) measurement-device-independent (MDI) quantum cryptography is now heading towards solving the practical problem of implementing scalable quantum networks. In this paper, we show that a solution can come from deploying an optical amplifier in the CV-MDI system, aiming to establish a high-rate quantum network. We suggest an improved CV-MDI protocol using the EPR states coupled with optical amplifiers. It can implement a practical quantum network scheme, where the legal participants create the secret correlations by using EPR states connecting to an untrusted relay via insecure links and applying the multi-entangled Greenberger-Horne-Zeilinger (GHZ) state analysis at relay station. Despite the possibility that the relay could be completely tampered with and imperfect links are subject to the powerful attacks, the legal participants are still able to extract a secret key from network communication. The numerical simulation indicates that the quantum network communication can be achieved in an asymmetric scenario, fulfilling the demands of a practical quantum network. Furthermore, we show that the use of optical amplifiers can compensate the inherent imperfections and improve the secret key rate of the CV-MDI system.
Role of measurement in feedback-controlled quantum engines
Yi, Juyeon; Kim, Yong Woon
2018-01-01
In feedback controls, measurement is an essential step in designing protocols according to outcomes. For quantum mechanical systems, measurement has another effect; to supply energy to the measured system. We verify that in feedback-controlled quantum engines, measurement plays a dual role; not only as an auxiliary to perform feedback control but also as an energy supply to drive the engines. We consider a specific engine cycle exploiting feedback control followed by projective measurement and show that the maximum bound of the extractable work is set by both the efficacy of the feedback control and the energy change caused by projective measurement. We take a concrete example of an engine using an immobile spin-1/2 particle as a working substance and suggest two possible scenarios for work extraction.
Problems in classical and quantum mechanics extracting the underlying concepts
Kelley, J Daniel
2017-01-01
This book is a collection of problems intended to aid students in their graduate courses in physics and in preparing for the PhD qualifying exam. Thus, the included problems are of the type that could be on a qualifying exam or are problems that are meant to elucidate a principle that is important for the exam. Unlike other compilations of problems, the problems in this text are placed in the broader context of the subject. The goal of the book is to develop the problem solving skills of the reader to insure a complete understanding of the physics. Problems and solutions are presented in detail, and, additionally, their significance is discussed within the context of the physical principle(s) that they illustrate. The solution of the problem is only the beginning of the learning process--it is in manipulating the solution and changing the parameters that a great deal of insight can be gleaned. This technique is referred to by the authors as "massaging the problem," and it is a technique that the authors have ...
Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics
Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert
1995-05-01
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.
Oxide double quantum dot - an answer to the qubit problem?
Yarlagadda, Sudhakar; Dey, Amit
We propose that oxide-based double quantum dots with only one electron (tunnelling between the dots) can be regarded as a qubit with little decoherence; these dots can possibly meet future challenges of miniaturization. The tunnelling of the eg electron between the dots and the attraction between the electron and the hole on adjacent dots can be modelled as an anisotropic Heisenberg interaction between two spins with the total z-component of the spins being zero. We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for SzT (the z-component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the polaron dynamics through a non-Markovian quantum master equation, we find that the system manifests a small amount of decoherence that decreases both with increasing nonadiabaticity and with enhancing strength of coupling g. Recently I got an invitation to visit Argonne National Lab from Jan./2106 to end of March/2016. I thought I would give a talk at APS March meeting. Please accept the submission.
A cost-effective measurement-device-independent quantum key distribution system for quantum networks
Valivarthi, Raju; Zhou, Qiang; John, Caleb; Marsili, Francesco; Verma, Varun B.; Shaw, Matthew D.; Nam, Sae Woo; Oblak, Daniel; Tittel, Wolfgang
2017-12-01
We experimentally realize a measurement-device-independent quantum key distribution (MDI-QKD) system. It is based on cost-effective and commercially available hardware such as distributed feedback lasers and field-programmable gate arrays that enable time-bin qubit preparation and time-tagging, and active feedback systems that allow for compensation of time-varying properties of photons after transmission through deployed fiber. We examine the performance of our system, and conclude that its design does not compromise performance. Our demonstration paves the way for MDI-QKD-based quantum networks in star-type topology that extend over more than 100 km distance.
Time-dependent problems in quantum-mechanical state reconstruction
International Nuclear Information System (INIS)
Leonhardt, U.; Bardroff, P. J.
1997-01-01
We study the state reconstruction of wave packets that travel in time-dependent potentials. We solve the problem for explicitly time-dependent potentials. We solve the problem for explicitly time-dependent harmonic oscillators and sketch a general adaptive technique for finding the wave function that matches and observed evolution. (authors)
Measurement and quasi-states in quantum mechanics
International Nuclear Information System (INIS)
Harper, C.D.
1987-01-01
Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems; interacting quantum-mechanical systems do not possess states, so their states cannot collapse. This dissertation shows that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it. A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system give rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state. The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value
Quantum optical measurements with undetected photons through vacuum field indistinguishability.
Lee, Sun Kyung; Yoon, Tai Hyun; Cho, Minhaeng
2017-07-26
Quantum spectroscopy and imaging with undetected idler photons have been demonstrated by measuring one-photon interference between the corresponding entangled signal fields from two spontaneous parametric down conversion (SPDC) crystals. In this Report, we present a new quantum optical measurement scheme utilizing three SPDC crystals in a cascading arrangement; here, neither the detection of the idler photons which interact with materials of interest nor their conjugate signal photons which do not interact with the sample is required. The coherence of signal beams in a single photon W-type path-entangled state is induced and modulated by indistinguishabilities of the idler beams and crucially the quantum vacuum fields. As a result, the optical properties of materials or objects interacting with the idler beam from the first SPDC crystal can be measured by detecting second-order interference between the signal beams generated by the other two SPDC crystals further down the set-up. This gedankenexperiment illustrates the fundamental importance of vacuum fields in generating an optical tripartite entangled state and thus its crucial role in quantum optical measurements.
On the Interpretation of Measurement Within the Quantum Theory
Cooper, Leon N.; Van Vechten, Deborah
1969-01-01
In interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory. The entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrodinger equation. (RR)
Dynamics of 'quantumness' measures in the decohering harmonic ...
Indian Academy of Sciences (India)
2016-07-26
Jul 26, 2016 ... are relative measures, using different definitions of the distance between the given quantum states and the set ..... the correspondence principle on the face of it, as they ..... validity of using the negativity – ηW – as an absolute.
Directly Measuring the Degree of Quantum Coherence using Interference Fringes
Wang, Yi-Tao; Tang, Jian-Shun; Wei, Zhi-Yuan; Yu, Shang; Ke, Zhi-Jin; Xu, Xiao-Ye; Li, Chuan-Feng; Guo, Guang-Can
2017-01-01
Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior—the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l1 norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.
Uncertainty relation and simultaneous measurements in quantum theory
International Nuclear Information System (INIS)
Busch, P.
1982-01-01
In this thesis the question for the interpretation of the uncertainty relation is picked up, and a program for the justification of its individualistic interpretation is formulated. By means of quantum mechanical models for the position and momentum measurement a justification of the interpretaton has been tried by reconstruction of the origin of the uncertainties from the conditions of the measuring devices and the determination of the relation of the measured results to the object. By means of a model of the common measurement it could be shown how the uncertainty relation results from the not eliminable mutual disturbance of the devices and the uncertainty relation for the measuring system. So finally the commutation relation is conclusive. For the illustration the split experiment is discussed, first according to Heisenberg with fixed split, then for the quantum mechanical, movable split (Bohr-Einstein). (orig./HSI) [de
Quantum Measurement Backaction and Upconverting Microwave Signals with Mechanical Resonators
Peterson, R. W.
The limits of optical measurement and control of mechanical motion are set by the quantum nature of light. The familiar shot noise limit can be avoided by increasing the optical power, but at high enough powers, the backaction of the randomly-arriving photons' radiation pressure can grow to become the dominant force on the system. This thesis will describe an experiment showing how backaction limits the laser cooling of macroscopic drumhead membranes, as well as work on how these membranes can be used to upconvert microwave signals to optical frequencies, potentially preserving the fragile quantum state of the upconverted signal.
Observing quantum trajectories: From Mott’s problem to quantum Zeno effect and back
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de, E-mail: maurice.de.gosson@univie.ac.at [University of Vienna, Faculty of Mathematics (NuHAG) Oskar-Morgenstern-Platz 1, 1090 Vienna (Austria); Hiley, Basil [Physics Department, University College, London, Gower Street, London WC1E 6BT (United Kingdom); TPRU, Birkbeck, University of London, Malet Street, London WC1E 7HX (United Kingdom); Cohen, Eliahu [H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL (United Kingdom)
2016-11-15
The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct “trajectories” in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a “quantum trajectory” first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories differ from those produced in a typical particle tracker and the key to this difference lies in the active suppression of the quantum potential necessary to produce Mott-type trajectories. We show, using a rigorous mathematical argument, how the active suppression of this potential arises. Finally we discuss in detail how this suppression also accounts for the quantum Zeno effect.
Information-disturbance tradeoff in quantum measurements
International Nuclear Information System (INIS)
Maccone, Lorenzo
2006-01-01
We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states
Control and Measurement of an Xmon with the Quantum Socket
McConkey, T. G.; Bejanin, J. H.; Earnest, C. T.; McRae, C. R. H.; Rinehart, J. R.; Weides, M.; Mariantoni, M.
The implementation of superconducting quantum processors is rapidly reaching scalability limitations. Extensible electronics and wiring solutions for superconducting quantum bits (qubits) are among the most imminent issues to be tackled. The necessity to substitute planar electrical interconnects (e.g., wire bonds) with three-dimensional wires is emerging as a fundamental pillar towards scalability. In a previous work, we have shown that three-dimensional wires housed in a suitable package, named the quantum socket, can be utilized to measure high-quality superconducting resonators. In this work, we set out to test the quantum socket with actual superconducting qubits to verify its suitability as a wiring solution in the development of an extensible quantum computing architecture. To this end, we have designed and fabricated a series of Xmon qubits. The qubits range in frequency from about 6 to 7 GHz with anharmonicity of 200 MHz and can be tuned by means of Z pulses. Controlling tunable Xmons will allow us to verify whether the three-dimensional wires contact resistance is low enough for qubit operation. Qubit T1 and T2 times and single qubit gate fidelities are compared against current standards in the field.
Solved and unsolved problems in relativistic quantum chemistry
International Nuclear Information System (INIS)
Kutzelnigg, Werner
2012-01-01
Graphical abstract: The graphical abstract represents the Dirac-Coulomb Hamiltonian in Fock space in a diagrammatic notation. A line (vertical or slanted) with an upgoing arrow represents an eletron, with a downgoing arrow a positron. A cross in the first line means the potential created by a nucleus, a broken line represents the Coulomb interaction between electrons and positrons. Highlights: ► Relativistic many-electron theory needs a Fock space and a field-dependent vacuum. ► A good starting point is QED in Coulomb gauge without transversal photons. ► The Dirac underworld picture is obsolete. ► A kinetically balanced even-tempered Gaussian basis is complete. ► ‘Quantum chemistry in Fock space is preferable over QED. - Abstract: A hierarchy of approximations in relativistic many-electron theory is discussed that starts with the Dirac equation and its expansion in a kinetically balanced basis, via a formulation of non-interacting electrons in Fock space (which is the only consistent way to deal with negative-energy states). The most straightforward approximate Hamiltonian for interacting electrons is derived from quantum electrodynamics (QED) in Coulomb gauge with the neglect of transversal photons. This allows an exact (non-perturbative) decoupling of the electromagnetic field from the fermionic field. The electric interaction of the fermions is non-retarded and non-quantized. The quantization of the fermionic field leads to a polarizable vacuum. The simplest (but somewhat problematic) approximation is a no-pair projected theory with external-field projectors. The Dirac-Coulomb operator in configuration space (first quantization) is not acceptable, even if the Brown–Ravenhall disease is much less virulent than often claimed. Effects of transversal photons, such as the Breit interaction and renormalized self-interaction can be taken care of perturbatively at the end, but there are still many open questions.
Zurek, Wojciech Hubert
2009-03-01
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the quantum fragility of a state of a single quantum system can lead to the classical robustness of states in their correlated multitude; shows how effective `wave-packet collapse' arises as a result of the proliferation throughout the environment of imprints of the state of the system; and provides a framework for the derivation of Born's rule, which relates the probabilities of detecting states to their amplitudes. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem.
Problems in continuous dose rate measurement
International Nuclear Information System (INIS)
Yoshioka, Mitsuo
1983-01-01
The system of continuous dose rate measurement in Fukui Prefecture is described. A telemeter system was constructed in October, 1976, and it has been operated since 1977. Observation has been made at 11 observation stations in the Prefecture. In addition to the continuous measurement of dose rate by using NaI(T1)-DBM systems, the ionization chambers for high dose rate were installed, and also meteorological data have been collected. The detectors are covered with 1 mm thick aluminum designed so that the absorption of external radiation is kept as small as possible. To keep the environmental temperature of the detectors constant, constant temperature wind blow is made. With these consideration, the measurement of Xe-133 is possible, and the standard deviation of yearly dose is around 0.4 mR/Y. By measuring DBM transmission rate, the contribution of Xe-133, which comes from the exhaust pumps in power plants, can be detected. The problems of this system are as follows. First of all, the characteristics of the system must meet the purpose of dose monitoring. The system must detect the dose less than the target value to be achieved. The second is the selection of measuring systems to be set. The system is still not unified, and it is difficult to exchange data between different stations. Finally, the method of data analysis is not yet unified. Manuals or guide-books for this purpose are necessary for the mutual comparison of the data from the stations in different districts. (Kato, T.)
Ghost problem of quantum field theories with higher derivatives
International Nuclear Information System (INIS)
Gavrielides, A.; Kuo, T.K.; Lee, S.Y.
1976-01-01
Second-order theories, i.e., theories described by Lagrangians quadratic in second derivatives of the fields, are carefully examined and their ghost problems are isolated and clearly exhibited. In particular, theories with gauge symmetry are shown to have precisely the same ghost problems as theories without gauge symmetry. It is also shown that massless theories of the same nature are the limit of massive theories containing ghost states
Compiling Planning into Quantum Optimization Problems: A Comparative Study
2015-06-07
to SAT, and then reduces higher order terms to quadratic terms through a series of gadgets . Our mappings allow both positive and negative preconditions...to its being specific to this type of problem) and likely benefits from an homogeneous parameter setting (Venturelli et al. 2014), as it generates a...Guzik, A. 2013. Resource efficient gadgets for compiling adiabatic quan- tum optimization problems. Annalen der Physik 525(10- 11):877–888. Blum, A
Verifiable Measurement-Only Blind Quantum Computing with Stabilizer Testing.
Hayashi, Masahito; Morimae, Tomoyuki
2015-11-27
We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and, therefore, Alice can obtain the correct computation result. Regarding the security, whatever Bob does, Bob cannot get any information about Alice's computation because of the no-signaling principle. Furthermore, malicious Bob does not necessarily send the copies of the correct graph state, but Alice can check the correctness of Bob's state by directly verifying the stabilizers of some copies.
Nonlinearities in the quantum measurement process of superconducting qubits
International Nuclear Information System (INIS)
Serban, Ioana
2008-05-01
The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on
Nonlinearities in the quantum measurement process of superconducting qubits
Energy Technology Data Exchange (ETDEWEB)
Serban, Ioana
2008-05-15
The work described in this thesis focuses on the investigation of decoherence and measurement backaction, on the theoretical description of measurement schemes and their improvement. The study presented here is centered around quantum computing implementations using superconducting devices and most important, the Josephson effect. The measured system is invariantly a qubit, i. e. a two-level system. The objective is to study detectors with increasing nonlinearity, e. g. coupling of the qubit to the frequency a driven oscillator, or to the bifurcation amplifier, to determine the performance and backaction of the detector on the measured system and to investigate the importance of a strong qubit-detector coupling for the achievement of a quantum non-demolition type of detection. The first part gives a very basic introduction to quantum information, briefly reviews some of the most promising physical implementations of a quantum computer before focusing on the superconducting devices. The second part presents a series of studies of different qubit measurements, describing the backaction of the measurement onto the measured system and the internal dynamics of the detector. Methodology adapted from quantum optics and chemical physics (master equations, phase-space analysis etc.) combined with the representation of a complex environment yielded a tool capable of describing a nonlinear, non-Markovian environment, which couples arbitrarily strongly to the measured system. This is described in chapter 3. Chapter 4 focuses on the backaction on the qubit and presents novel insights into the qubit dephasing in the strong coupling regime. Chapter 5 uses basically the same system and technical tools to explore the potential of a fast, strong, indirect measurement, and determine how close such a detection would ideally come to the quantum non-demolition regime. Chapter 6 focuses on the internal dynamics of a strongly driven Josephson junction. The analytical results are based on
The quantum N-body problem in the mean-field and semiclassical regime.
Golse, François
2018-04-28
The present work discusses the mean-field limit for the quantum N -body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).
The Problem of Time in Quantum Cosmology: A Decoherent Histories View
International Nuclear Information System (INIS)
Christodoulakis, Theodosios; Wallden, Petros
2011-01-01
The problem of time in quantum gravity arises due to the diffeomorphisms invariance of the theory and appears via the Hamiltonian constraint, in the canonical quantizations. There is a need for a description where one can ask some timeless questions that still encode some sense of temporality. The decoherent histories approach to quantum theory, already at the kinematical level admits an internal time. Several alternative proposals for resolving the problem of time via the decoherent histories, exist, and in this contribution we focus on one particular and examine how it manifests itself at some simple cosmological models.
Solving Problem of Graph Isomorphism by Membrane-Quantum Hybrid Model
Directory of Open Access Journals (Sweden)
Artiom Alhazov
2015-10-01
Full Text Available This work presents the application of new parallelization methods based on membrane-quantum hybrid computing to graph isomorphism problem solving. Applied membrane-quantum hybrid computational model was developed by authors. Massive parallelism of unconventional computing is used to implement classic brute force algorithm efficiently. This approach does not suppose any restrictions of considered graphs types. The estimated performance of the model is less then quadratic that makes a very good result for the problem of \\textbf{NP} complexity.
Quantum Jarzynski equality with multiple measurement and ...
Indian Academy of Sciences (India)
three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with ... theorems have important application in nanotechnology and nanophysics. One of the ... Thus the joint probability of state being in |i0〉 and |iτ 〉 is.
Two-particle quantum walks applied to the graph isomorphism problem
International Nuclear Information System (INIS)
Gamble, John King; Friesen, Mark; Zhou Dong; Joynt, Robert; Coppersmith, S. N.
2010-01-01
We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in which one wishes to determine whether two graphs are isomorphic (related to each other by a relabeling of the graph vertices), and focus on a class of graphs with particularly high symmetry called strongly regular graphs (SRGs). We study the Green's functions that characterize the dynamical evolution single-particle and two-particle quantum walks on pairs of nonisomorphic SRGs and show that interacting particles can distinguish nonisomorphic graphs that noninteracting particles cannot. We obtain the following specific results. (1) We prove that quantum walks of two noninteracting particles, fermions or bosons, cannot distinguish certain pairs of nonisomorphic SRGs. (2) We demonstrate numerically that two interacting bosons are more powerful than single particles and two noninteracting particles, in that quantum walks of interacting bosons distinguish all nonisomorphic pairs of SRGs that we examined. By utilizing high-throughput computing to perform over 500 million direct comparisons between evolution operators, we checked all tabulated pairs of nonisomorphic SRGs, including graphs with up to 64 vertices. (3) By performing a short-time expansion of the evolution operator, we derive distinguishing operators that provide analytic insight into the power of the interacting two-particle quantum walk.
XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints
Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.
2018-01-01
Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.
Algebraic and algorithmic frameworks for optimized quantum measurements
DEFF Research Database (Denmark)
Laghaout, Amine; Andersen, Ulrik Lund
2015-01-01
von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are, however, static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can...... be overcome by "wrapping" the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup specific. We shall here develop a unified framework...
DEFF Research Database (Denmark)
Shirokov, M. E.; Shulman, Tatiana
2014-01-01
We give a detailed description of a low-dimensional quantum channel (input dimension 4, Choi rank 3) demonstrating the symmetric form of superactivation of one-shot quantum zero-error capacity. This property means appearance of a noiseless (perfectly reversible) subchannel in the tensor square...... of a channel having no noiseless subchannels. Then we describe a quantum channel with an arbitrary given level of symmetric superactivation (including the infinite value). We also show that superactivation of one-shot quantum zero-error capacity of a channel can be reformulated in terms of quantum measurement...
Development of measurement protocols for quantum magnetometry
DEFF Research Database (Denmark)
Stark, Alexander
and protocols to enhance the lifetime and the coherences of the NV center with the overall goal of enhancing the capabilities of this sensor in the field of magnetometry. In order to realize complex protocols, a sophisticated software control of the measurement setup is required. A general software framework......, is serving as rigorous framework to reduce the complexity of the setup configuration by a fundamental separation of tasks. As a consequence, the general idea of this framework is not limited to experiments with color centers in diamond, but can find application in any laboratory environment. The measurement...... of magnetic fields in the high-frequency GHz regimes is challenging. In this thesis, a continuous dynamical decoupling protocol is developed and implemented, which extends the capabilities of the NV sensor to probe GHz signals with a narrow bandwidth. Moreover, the protocol protects the system from noise...
Continuous quantum measurements and the action uncertainty principle
Mensky, Michael B.
1992-09-01
The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral “in finite limits”). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is δ S≳ℏ, where S is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is |∫{/' t″ }(δ S[ q]/δ q( t))Δ q( t) dt|≃ℏ, where the paths [ q] and [Δ q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as Δ(Equation) Δ(Path) ≃ ℏ. This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement.
Measurement of photomultiplier effective quantum efficiency
International Nuclear Information System (INIS)
Arshad, S.; Gowers, C.; Nielsen, P.
1998-07-01
The JET divertor LIDAR system, is being modified to perform measurements of plasma edge electron temperature and density in the new gas-box divertor configuration. The change involves raising the line of sight from the divertor region so that the laser beam passes through the plasma edge reaching a depth of ∼ 5 cm inside the boundary. Changes are also being made to the detection system. This currently employs a grating, spectrometer and a streak camera. The new system will contain a 4-channel filter spectrometer with microchannel plate (MCP) photomuItipliers
New methods for the measurement and alteration of quantum states
International Nuclear Information System (INIS)
Steuernagel, O.
1996-01-01
Themes of this thesis are the mathematical representation, measurement-technical reconstruction, and preparation of quantum states as well as their alteration by measurement. The main topics of the considerations are quantum-mechanical system states, the complet description of which pursues by means of density operators. The first chapter presents a general mathematical scheme for the representaion of density operators by means of projection operators. The second chapter explains a scheme for the syntehsis of Fock states by means of a linear mixer. The third chapter answers the question, whether spontaneous emitted light, which is emitted by an atom with large spatial extension, can show self-interferences and lets conclude on thee coherent structure of the c.m. wave function of the emitting atom. The last chapter reconstructs measurement results on the coherence loss of atoms in an atomic-beam experiment by spontaneous emission in the language of the density-operator formalism
Bell's theorem and the measurement problem: reducing two mysteries to one?
International Nuclear Information System (INIS)
Cavalcanti, Eric G.
2016-01-01
In light of a recent reformulation of Bell's theorem from causal principles by Wiseman and the author, I argue that the conflict between quantum theory and relativity brought up by Bell's work can be softened by a revision of our classical notions of causation. I review some recent proposals for a quantum theory of causation that make great strides towards that end, but highlight a property that is shared by all those theories that would not have satisfied Bell's realist inclinations. They require (implicitly or explicitly) agent-centric notions such as “controllables” and “uncontrollables”, or “observed” and “unobserved”. Thus they relieve the tensions around Bell's theorem by highlighting an issue more often associated with another deep conceptual issue in quantum theory: the measurement problem. Rather than rejecting those terms, however, I argue that we should understand why they seem to be, at least at face-value, needed in order to reach compatibility between quantum theory and relativity. This seems to suggest that causation, and thus causal structure, are emergent phenomena, and lends support to the idea that a resolution of the conflict between quantum theory and relativity necessitates a solution to the measurement problem. (paper)
Solution to the sign problem in a frustrated quantum impurity model
Energy Technology Data Exchange (ETDEWEB)
Hann, Connor T., E-mail: connor.hann@yale.edu [Department of Physics, Box 90305, Duke University, Durham, NC 27708 (United States); Huffman, Emilie [Department of Physics, Box 90305, Duke University, Durham, NC 27708 (United States); Chandrasekharan, Shailesh [Department of Physics, Box 90305, Duke University, Durham, NC 27708 (United States); Center for High Energy Physics, Indian Institute of Science, Bangalore, 560 012 (India)
2017-01-15
In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weight configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.
A Quantum Non-Demolition Parity measurement in a mixed-species trapped-ion quantum processor
Marinelli, Matteo; Negnevitsky, Vlad; Lo, Hsiang-Yu; Flühmann, Christa; Mehta, Karan; Home, Jonathan
2017-04-01
Quantum non-demolition measurements of multi-qubit systems are an important tool in quantum information processing, in particular for syndrome extraction in quantum error correction. We have recently demonstrated a protocol for quantum non-demolition measurement of the parity of two beryllium ions by detection of a co-trapped calcium ion. The measurement requires a sequence of quantum gates between the three ions, using mixed-species gates between beryllium hyperfine qubits and a calcium optical qubit. Our work takes place in a multi-zone segmented trap setup in which we have demonstrated high fidelity control of both species and multi-well ion shuttling. The advantage of using two species of ion is that we can individually manipulate and read out the state of each ion species without disturbing the internal state of the other. The methods demonstrated here can be used for quantum error correcting codes as well as quantum metrology and are key ingredients for realizing a hybrid universal quantum computer based on trapped ions. Mixed-species control may also enable the investigation of new avenues in quantum simulation and quantum state control. left the group and working in a company now.
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group
International Nuclear Information System (INIS)
Wang, S.J.
1993-04-01
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)
Multi-qubit parity measurement in circuit quantum electrodynamics
International Nuclear Information System (INIS)
DiVincenzo, David P; Solgun, Firat
2013-01-01
We present a concept for performing direct parity measurements on three or more qubits in microwave structures with superconducting resonators coupled to Josephson-junction qubits. We write the quantum-eraser conditions that must be fulfilled for the parity measurements as requirements for the scattering phase shift of our microwave structure. We show that these conditions can be fulfilled with present-day devices. We present one particular scheme, implemented with two-dimensional cavity techniques, in which each qubit should be coupled equally to two different microwave cavities. The magnitudes of the couplings that are needed are in the range that has been achieved in current experiments. A quantum calculation indicates that the measurement is optimal if the scattering signal can be measured with near single-photon sensitivity. A comparison with an extension of a related proposal from cavity optics is presented. We present a second scheme, for which a scalable implementation of the four-qubit parities of the surface quantum error correction code can be envisioned. It uses three-dimensional cavity structures, using cavity symmetries to achieve the necessary multiple resonant modes within a single resonant structure. (paper)
Bolemon, Jay S.; Etzold, David J.
1974-01-01
Discusses the use of a small computer to solve self-consistent field problems of one-dimensional systems of two or more interacting particles in an elementary quantum mechanics course. Indicates that the calculation can serve as a useful introduction to the iterative technique. (CC)
Kinetic approach to the initial value problem in quantum field theory
International Nuclear Information System (INIS)
Lin Chi Yong; Toledo Piza, A.F.R. de.
1989-06-01
Time-dependente projection techniques developed to derive kinetic equations in the context of the quantum many-body problem are applied to φ 4 field theory. The approach is illustrated by working out the 0+1 dimensional case explicitly, including numerical solutions of the kinetic equations. Extension to higher dimensions is briefly discussed. (author) [pt
Quantum measurement of a rapidly rotating spin qubit in diamond.
Wood, Alexander A; Lilette, Emmanuel; Fein, Yaakov Y; Tomek, Nikolas; McGuinness, Liam P; Hollenberg, Lloyd C L; Scholten, Robert E; Martin, Andy M
2018-05-01
A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realizing a single qubit that can be measured and controlled during physical rotation is experimentally challenging. We demonstrate quantum control of a single nitrogen-vacancy (NV) center within a diamond rotated at 200,000 rpm, a rotational period comparable to the NV spin coherence time T 2 . We stroboscopically image individual NV centers that execute rapid circular motion in addition to rotation and demonstrate preparation, control, and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame and paves the way for the realization of single-qubit diamond-based rotation sensors.
Memory-assisted measurement-device-independent quantum key distribution
International Nuclear Information System (INIS)
Panayi, Christiana; Razavi, Mohsen; Ma, Xiongfeng; Lütkenhaus, Norbert
2014-01-01
A protocol with the potential of beating the existing distance records for conventional quantum key distribution (QKD) systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of measurement-device-independent QKD, which only requires optical source equipment at the user's end. For certain memories with short access times, our scheme allows a higher repetition rate than that of quantum repeaters with single-mode memories, thereby requiring lower coherence times. By accounting for various sources of nonideality, such as memory decoherence, dark counts, misalignment errors, and background noise, as well as timing issues with memories, we develop a mathematical framework within which we can compare QKD systems with and without memories. In particular, we show that with the state-of-the-art technology for quantum memories, it is potentially possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations. (paper)
Applications of the renormalization group approach to problems in quantum field theory
International Nuclear Information System (INIS)
Renken, R.L.
1985-01-01
The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical
Vol. 1: Physics of Elementary Particles and Quantum Field Theory. General Problems
International Nuclear Information System (INIS)
Sitenko, A.
1993-01-01
Problems of modern physics and the situation with physical research in Ukraine are considered. Programme of the conference includes scientific and general problems. Its proceedings are published in 6 volumes. The papers presented in this volume refer to elementary particle physics and quantum field theory. The main attention is paid to the following problems: - development of science in Ukraine and its role in the state structures; - modern state of scientific research in Ukraine; - education and training of specialists; - history of Ukrainian physics and contribution of Ukrainian scientists in the world science; - problems of the Ukrainian scientific terminology
Measure theoretical approach to recurrent properties for quantum dynamics
International Nuclear Information System (INIS)
Otobe, Yoshiki; Sasaki, Itaru
2011-01-01
Poincaré's recurrence theorem, which states that every Hamiltonian dynamics enclosed in a finite volume returns to its initial position as close as one wishes, is a mathematical basis of statistical mechanics. It is Liouville's theorem that guarantees that the dynamics preserves the volume on the state space. A quantum version of Poincaré's theorem was obtained in the middle of the 20th century without any volume structures of the state space (Hilbert space). One of our aims in this paper is to establish such properties of quantum dynamics from an analog of Liouville's theorem, namely, we will construct a natural probability measure on the Hilbert space from a Hamiltonian defined on the space. Then we will show that the measure is invariant under the corresponding Schrödinger flow. Moreover, we show that the dynamics naturally causes an infinite-dimensional Weyl transformation. It also enables us to discuss the ergodic properties of such dynamics. (paper)
Applications of quantum measurement in single and many body systems
International Nuclear Information System (INIS)
Steixner, V.
2010-01-01
This thesis contains a study about the influence of the back action of a signal emitted by a trapped ion onto itself. The continuous measurement signal is used to alter the motional state of the ion, corresponding to classical friction, in order to cool the ion. The quantum mechanical evolution of the ion with the help of stochastic Schroedinger- and master equations is explored, as well as experimental results. A second method of feedback to obtain the momentum necessary for cooling by means of electromagnetically induced transparency is discussed next. This method allows for a theoretical cooling down to the motional ground state. In a second part of the thesis, the measurement of particle currents in optical lattices is discussed. The usual method of measuring spatial correlations in a cold gas, the time-of-flight method, disadvantageously destroys the measured sample. Here a measurement scheme for atoms with an internal Lambda level structure, coupled with lasers as a Raman transition, is used instead. The measured photons are transformed with the help of homodyne detection into a continuous photon current proportional to the particle current. This thesis contains numerical and analytical calculations for this measurement process and the back action on the measured system. As an application example, the measurement of superfluid currents in a ring optical lattice is described, as well as the entanglement of two of these macroscopic quantum objects. (author) [de
Miller, Jacob; Sanders, Stephen; Miyake, Akimasa
2017-12-01
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable advantage in quantum devices without demanding quantum error correction, which is crucial for prolonging the coherence time of qubits. We propose a model device made of locally interacting multiple qubits, designed such that simultaneous single-qubit measurements on it can output probability distributions whose average-case sampling is classically intractable, under similar assumptions as the sampling of noninteracting bosons and instantaneous quantum circuits. Notably, in contrast to these previous unitary-based realizations, our measurement-based implementation has two distinctive features. (i) Our implementation involves no adaptation of measurement bases, leading output probability distributions to be generated in constant time, independent of the system size. Thus, it could be implemented in principle without quantum error correction. (ii) Verifying the classical intractability of our sampling is done by changing the Pauli measurement bases only at certain output qubits. Our usage of random commuting quantum circuits in place of computationally universal circuits allows a unique unification of sampling and verification, so they require the same physical resource requirements in contrast to the more demanding verification protocols seen elsewhere in the literature.
The three-body problem in quantum mechanics
International Nuclear Information System (INIS)
Antunes, A.C.B.
1973-01-01
Different methods used in the analysis of the scattering of an elementary particle by a system of two bound particles are compared. All particles are considered spinless and distinguishable from each other. Two approaches are used in the treatment of the problem. In the first method we build an effective - potential which accounts for the interaction of the incident particle with the bound system. The second approach consists in treating the target as a system of two particles, whose momentum distribution is given by the bound state wavefunction. The three body system is then treated by the techniques of the multiple scattering series and of Glauber theory. (author)
Entanglement measure for general pure multipartite quantum states
International Nuclear Information System (INIS)
Heydari, Hoshang; Bjoerk, Gunnar
2004-01-01
We propose an explicit formula for a measure of entanglement of pure multipartite quantum states. We discuss the mathematical structure of the measure and give a brief explanation of its physical motivation. We apply the measure on some pure, tripartite, qubit states and demonstrate that, in general, the entanglement can depend on what actions are performed on the various subsystems, and specifically if the parties in possession of the subsystems cooperate or not. We also give some simple but illustrative examples of the entanglement of four-qubit and m-qubit states
Covariance problem in two-dimensional quantum chromodynamics
International Nuclear Information System (INIS)
Hagen, C.R.
1979-01-01
The problem of covariance in the field theory of a two-dimensional non-Abelian gauge field is considered. Since earlier work has shown that covariance fails (in charged sectors) for the Schwinger model, particular attention is given to an evaluation of the role played by the non-Abelian nature of the fields. In contrast to all earlier attempts at this problem, it is found that the potential covariance-breaking terms are identical to those found in the Abelian theory provided that one expresses them in terms of the total (i.e., conserved) current operator. The question of covariance is thus seen to reduce in all cases to a determination as to whether there exists a conserved global charge in the theory. Since the charge operator in the Schwinger model is conserved only in neutral sectors, one is thereby led to infer a probable failure of covariance in the non-Abelian theory, but one which is identical to that found for the U(1) case
Quantum information and the problem of mechanisms of biological evolution.
Melkikh, Alexey V
2014-01-01
One of the most important conditions for replication in early evolution is the de facto elimination of the conformational degrees of freedom of the replicators, the mechanisms of which remain unclear. In addition, realistic evolutionary timescales can be established based only on partially directed evolution, further complicating this issue. A division of the various evolutionary theories into two classes has been proposed based on the presence or absence of a priori information about the evolving system. A priori information plays a key role in solving problems in evolution. Here, a model of partially directed evolution, based on the learning automata theory, which includes a priori information about the fitness space, is proposed. A potential repository of such prior information is the states of biologically important molecules. Thus, the need for extended evolutionary synthesis is discussed. Experiments to test the hypothesis of partially directed evolution are proposed. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Classical universe emerging from quantum cosmology without horizon and flatness problems
Energy Technology Data Exchange (ETDEWEB)
Fathi, M.; Jalalzadeh, S. [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of); Moniz, P.V. [Centro de Matematica e Aplicacoes-UBI, Covilha (Portugal); Universidade da Beira Interior, Departmento de Fisica, Covilha (Portugal)
2016-10-15
We apply the complex de Broglie-Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007), Gozzi (Phys Lett B 165: 351, 1985), Bhalla et al. (Am J Phys 65: 1187, 1997) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems. (orig.)
Analysis of Green's functions and stability problem in models of quantum field theory with solitons
International Nuclear Information System (INIS)
Raczka, R.; Roszkowski, L.
1983-10-01
A class of models of quantum field theory for a multiplet phi-vector=(phi 1 ,...,phisub(N)) of real scalar fields, possessing a particle-like classical solution phi-vector 0 , is considered. A new formula for generating functional for time-ordered Green's functions in terms of effective propagators is derived. The problem of classical and quantum stability is analyzed in detail. It is shown by partly non-perturbative analysis that in the considered models the excited states of mesons do exist and form the trajectories in the plane mass 2 -spin. These trajectories are linear or approximately linear like experimental trajectories. (author)
Many-body problem in quantum mechanics and quantum statistical mechanics
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/
Walls, D F
2007-01-01
Quantum Optics gives a comprehensive coverage of developments in quantum optics over the past years. In the early chapters the formalism of quantum optics is elucidated and the main techniques are introduced. These are applied in the later chapters to problems such as squeezed states of light, resonance fluorescence, laser theory, quantum theory of four-wave mixing, quantum non-demolition measurements, Bell's inequalities, and atom optics. Experimental results are used to illustrate the theory throughout. This yields the most comprehensive and up-to-date coverage of experiment and theory in quantum optics in any textbook. More than 40 exercises helps readers test their understanding and provide practice in quantitative problem solving.
On the connections between the classical and quantum-mechanical Kepler problems
International Nuclear Information System (INIS)
Dahl, J.P.; Jorgensen, T.G.
1993-01-01
The Runge-Lenz vector, which accounts for the accidental degeneracy of the non-relativistic Kepler problem, has been the subject matter of many studies, both in quantum mechanics and in classical mechanics. Much less attention has been paid to the Johnson-Lippmann operator which accounts for the accidental degeneracy of the relativistic Kepler problem in Dirac's quantum-mechanical description. In the present communication we discuss the properties of the Johnson-Lippmann operator. We show its relation to the non-relativistic Runge-Lenz vector and draw a connection to Sommerfield's early discussion of the relativistic Kepler problem. This enables us, inter alia, to give an explanation of the apparent coincidence of the energy expressions of the two theories
A review of the decoherent histories approach to the arrival time problem in quantum theory
International Nuclear Information System (INIS)
Yearsley, James M
2011-01-01
We review recent progress in understanding the arrival time problem in quantum mechanics, from the point of view of the decoherent histories approach to quantum theory. We begin by discussing the arrival time problem, focussing in particular on the role of the probability current in the expected classical solution. After a brief introduction to decoherent histories we review the use of complex potentials in the construction of appropriate class operators. We then discuss the arrival time problem for a particle coupled to an environment, and review how the arrival time probability can be expressed in terms of a POVM in this case. We turn finally to the question of decoherence of the corresponding histories, and we show that this can be achieved for simple states in the case of a free particle, and for general states for a particle coupled to an environment.
Practical quantum private query with better performance in resisting joint-measurement attack
Wei, Chun-Yan; Wang, Tian-Yin; Gao, Fei
2016-04-01
As a kind of practical protocol, quantum-key-distribution (QKD)-based quantum private queries (QPQs) have drawn lots of attention. However, joint-measurement (JM) attack poses a noticeable threat to the database security in such protocols. That is, by JM attack a malicious user can illegally elicit many more items from the database than the average amount an honest one can obtain. Taking Jacobi et al.'s protocol as an example, by JM attack a malicious user can obtain as many as 500 bits, instead of the expected 2.44 bits, from a 104-bit database in one query. It is a noticeable security flaw in theory, and would also arise in application with the development of quantum memories. To solve this problem, we propose a QPQ protocol based on a two-way QKD scheme, which behaves much better in resisting JM attack. Concretely, the user Alice cannot get more database items by conducting JM attack on the qubits because she has to send them back to Bob (the database holder) before knowing which of them should be jointly measured. Furthermore, JM attack by both Alice and Bob would be detected with certain probability, which is quite different from previous protocols. Moreover, our protocol retains the good characters of QKD-based QPQs, e.g., it is loss tolerant and robust against quantum memory attack.
Quantum mechanics problems in observer's mathematics
Energy Technology Data Exchange (ETDEWEB)
Khots, Boris; Khots, Dmitriy [Compressor Controls Corp, Des Moines, Iowa (United States); iMath Consulting LLC, Omaha, Nebraska (United States)
2012-11-06
This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.
Measuring Charge Carrier Diffusion in Coupled Colloidal Quantum Dot Solids
Zhitomirsky, David
2013-06-25
Colloidal quantum dots (CQDs) are attractive materials for inexpensive, room-temperature-, and solution-processed optoelectronic devices. A high carrier diffusion length is desirable for many CQD device applications. In this work we develop two new experimental methods to investigate charge carrier diffusion in coupled CQD solids under charge-neutral, i.e., undepleted, conditions. The methods take advantage of the quantum-size-effect tunability of our materials, utilizing a smaller-bandgap population of quantum dots as a reporter system. We develop analytical models of diffusion in 1D and 3D structures that allow direct extraction of diffusion length from convenient parametric plots and purely optical measurements. We measure several CQD solids fabricated using a number of distinct methods and having significantly different doping and surface ligand treatments. We find that CQD materials recently reported to achieve a certified power conversion efficiency of 7% with hybrid organic-inorganic passivation have a diffusion length of 80 ± 10 nm. The model further allows us to extract the lifetime, trap density, mobility, and diffusion coefficient independently in each material system. This work will facilitate further progress in extending the diffusion length, ultimately leading to high-quality CQD solid semiconducting materials and improved CQD optoelectronic devices, including CQD solar cells. © 2013 American Chemical Society.
Quantum analysis of the direct measurement of light waves
International Nuclear Information System (INIS)
Saldanha, Pablo L
2014-01-01
In a beautiful experiment performed about a decade ago, Goulielmakis et al (2004 Science 305 1267–69) made a direct measurement of the electric field of light waves. However, they used a laser source to produce the light field, whose quantum state has a null expectation value for the electric field operator, so how was it possible to measure this electric field? Here we present a quantum treatment for the f:2f interferometer used to calibrate the carrier–envelope phase of the light pulses in the experiment. We show how the special nonlinear features of the f:2f interferometer can change the quantum state of the electromagnetic field inside the laser cavity to a state with a definite oscillating electric field, explaining how the ‘classical’ electromagnetic field emerges in the experiment. We discuss that this experiment was, to our knowledge, the first demonstration of an absolute coherent superposition of different photon number states in the optical regime. (paper)
Quantum Jarzynski equality of measurement-based work extraction.
Morikuni, Yohei; Tajima, Hiroyasu; Hatano, Naomichi
2017-03-01
Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely, the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. Second, we derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The right-hand side of the equality reduces to unity for "natural" cyclic processes but fluctuates wildly for noncyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.
Problems at the interface between perturbative and nonperturbative quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.; Bodwin, G.T.; Lepage, G.P.
1983-06-01
Predictions based on perturbative QCD rest on three premises: (1) that hadronic interactions become weak in strength at small invariant separation; (2) that the perturbative expansion in α/sub s/(Q) is well-defined; and (3) factorization: all effects of collinear singularities, confinement, nonperturbative interactions, and bound state dynamics can be isolated at large momentum transfer in terms of structure functions, fragmentation functions, or in the case of exclusive processes, distribution amplitudes. The assumption that the perturbative expansion for hard scattering amplitudes converges has certainly not been demonstrated; in addition, there are serious ambiguities concerning the choice of renormalization scheme and scale choice Q 2 for the expansion in α/sub s/(Q 2 ). We will discuss a new procedure to at least partly rectify the latter problem. In the case of exclusive processes, the factorization of hadronic amplitudes at large momentum transfer in the form of distribution amplitudes convoluted with hard scattering quark-gluon subprocess amplitudes can be demonstrated systematically to all orders in α/sub s/(Q 2 ). In the case of inclusive reactions, factorization remains an ansatz; general all-orders proofs do not exist because of the complications of soft initial state interactions for hadron-induced processes; thus far factorization has only been verified to two loops beyond lowest order in a regime where the applicability of perturbation theory is in doubt. However, we shall show that a necessary condition for the validity of factorization in inclusive reactions is that the momentum transfer must be large compared to the (rest frame) length of the target. We review the present status of the factorization ansatz. 52 references
Entanglement measures in embedding quantum simulators with nuclear spins
Xin, Tao; Pedernales, Julen S.; Solano, Enrique; Long, Gui-Lu
2018-02-01
We implement an embedding quantum simulator (EQS) in nuclear spin systems. The experiment consists of a simulator of up to three qubits, plus a single ancillary qubit, where we are able to efficiently measure the concurrence and the three-tangle of two-qubit and three-qubit systems as they undergo entangling dynamics. The EQS framework allows us to drastically reduce the number of measurements needed for this task, which otherwise would require full-state reconstruction of the qubit system. Our simulator is built of the nuclear spins of four 13C atoms in a molecule of trans-crotonic acid manipulated with NMR techniques.
DEFF Research Database (Denmark)
Wu, Shengjun; Poulsen, Uffe Vestergaard; Mølmer, Klaus
2009-01-01
and the classical correlations and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present......We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum...... in the deterministic quantum computation with one quantum bit....
International Nuclear Information System (INIS)
Frackiewicz, Piotr
2011-01-01
We investigate implementations of the Eisert-Wilkens-Lewenstein (EWL) scheme of playing quantum games beyond strategic games. The scope of our research is decision problems, i.e. one-player extensive games. The research is based on the examination of their features when the decision problems are carried out via the EWL protocol. We prove that unitary operators can be adapted to play the role of strategies in decision problems with imperfect recall. Furthermore, we prove that unitary operators provide the decision maker with possibilities that are inaccessible for classical strategies.
Energy Technology Data Exchange (ETDEWEB)
Frackiewicz, Piotr, E-mail: P.Frackiewicz@impan.gov.pl [Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warsaw (Poland)
2011-08-12
We investigate implementations of the Eisert-Wilkens-Lewenstein (EWL) scheme of playing quantum games beyond strategic games. The scope of our research is decision problems, i.e. one-player extensive games. The research is based on the examination of their features when the decision problems are carried out via the EWL protocol. We prove that unitary operators can be adapted to play the role of strategies in decision problems with imperfect recall. Furthermore, we prove that unitary operators provide the decision maker with possibilities that are inaccessible for classical strategies.
Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function.
Vallone, Giuseppe; Dequal, Daniele
2016-01-29
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.
Indirect and two fold measurements in quantum mechanics
International Nuclear Information System (INIS)
Fer, Francis
1981-01-01
Keeping strictly in the positivist, probabilistic and hilbertian frame of quantum mechanics, the author develops a criticism of the accepted theory of indirect and twofold measurements. He shows that this theory cannot logically derive from the usual axiomatics, namely from the so-called reduction-of-state axiom. He proposes a modified statement (already used sometimes) of this axiom, which leads to a reliable theory of indirect and twofold measurements. The results are particularly: a) that a measurement made on a sub-system does not modify the mathematical representation of the complementary system, nor its prior probability distributions; b) that measurement is nothing else than an information which enables to correct the probabilities of further measurements according to the classical rules of the calculus of probabilities [fr
Fractal measures in a deep penetration problem
International Nuclear Information System (INIS)
Murthy, K.P.N.; Indira, R.; John, T.M.
1993-01-01
In the Monte Carlo simulation of a deep penetration problem the parameter, say b in the importance function must be assigned a value b' such that variance is minimum. If b b' the sample mean is still not reliable; but the sample fluctuations would be small and misleading, though the actual fluctuations are quite large. This is because the distribution of transmission has a tail which becomes prominent when b > b'. Considering a model deep penetration problem, and employing exact enumeration techniques, it is shown that in the limit of large biasing the long tailed distribution to the transmission is multifractal. (author). 5 refs., 3 figs
The quantum n-body problem in dimension d ⩾ n – 1: ground state
Miller, Willard, Jr.; Turbiner, Alexander V.; Escobar-Ruiz, M. A.
2018-05-01
We employ generalized Euler coordinates for the n body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual) mass-independent distances r ij and angles as remaining coordinates. We prove that the kinetic energy of the quantum n-body problem for can be written as the sum of three terms: (i) kinetic energy of centre-of-mass, (ii) the second order differential operator which depends on relative distances alone and (iii) the differential operator which annihilates any angle-independent function. The operator has a large reflection symmetry group and in variables is an algebraic operator, which can be written in terms of generators of the hidden algebra . Thus, makes sense of the Hamiltonian of a quantum Euler–Arnold top in a constant magnetic field. It is conjectured that for any n, the similarity-transformed is the Laplace–Beltrami operator plus (effective) potential; thus, it describes a -dimensional quantum particle in curved space. This was verified for . After de-quantization the similarity-transformed becomes the Hamiltonian of the classical top with variable tensor of inertia in an external potential. This approach allows a reduction of the dn-dimensional spectral problem to a -dimensional spectral problem if the eigenfunctions depend only on relative distances. We prove that the ground state function of the n body problem depends on relative distances alone.
Two path transport measurements on a triple quantum dot
Energy Technology Data Exchange (ETDEWEB)
Rogge, Maximilian C.; Haug, Rolf J. [Institut fuer Festkoerperphysik, Leibniz Universitaet Hannover, Appelstr. 2, 30167 Hannover (Germany)
2008-07-01
We present a novel triple quantum dot device made with local anodic oxidation on a GaAs/AlGaAs heterostructure. The geometry provides two path transport via a three lead setup with each lead connected to one of the three quantum dots. In addition charge detection is implemented via a quantum point contact. One lead is used as a common source contact, the other two are used as two separate drain contacts with independent current measurement. Thus two paths are formed with two dots in each path. Along both paths serial transport is observed at the triple points of the two corresponding dots. With four side gates a wide tunability is given. Thus the system can be tuned in and out of triple dot resonances. When all three dots come into resonance, quadruple points are formed with simultaneous transport along both paths. The data are analysed in combined two colour plots and compared to the charge detection showing sets of three different lines, one for each dot. This way the two path setup allows to investigate the transition from double dot physics to triple dot physics.
Directory of Open Access Journals (Sweden)
Ligang Cui
2013-01-01
Full Text Available The capacitated vehicle routing problem (CVRP is the most classical vehicle routing problem (VRP; many solution techniques are proposed to find its better answer. In this paper, a new improved quantum evolution algorithm (IQEA with a mixed local search procedure is proposed for solving CVRPs. First, an IQEA with a double chain quantum chromosome, new quantum rotation schemes, and self-adaptive quantum Not gate is constructed to initialize and generate feasible solutions. Then, to further strengthen IQEA's searching ability, three local search procedures 1-1 exchange, 1-0 exchange, and 2-OPT, are adopted. Experiments on a small case have been conducted to analyze the sensitivity of main parameters and compare the performances of the IQEA with different local search strategies. Together with results from the testing of CVRP benchmarks, the superiorities of the proposed algorithm over the PSO, SR-1, and SR-2 have been demonstrated. At last, a profound analysis of the experimental results is presented and some suggestions on future researches are given.
Direct quantum process tomography via measuring sequential weak values of incompatible observables.
Kim, Yosep; Kim, Yong-Su; Lee, Sang-Yun; Han, Sang-Wook; Moon, Sung; Kim, Yoon-Ho; Cho, Young-Wook
2018-01-15
The weak value concept has enabled fundamental studies of quantum measurement and, recently, found potential applications in quantum and classical metrology. However, most weak value experiments reported to date do not require quantum mechanical descriptions, as they only exploit the classical wave nature of the physical systems. In this work, we demonstrate measurement of the sequential weak value of two incompatible observables by making use of two-photon quantum interference so that the results can only be explained quantum physically. We then demonstrate that the sequential weak value measurement can be used to perform direct quantum process tomography of a qubit channel. Our work not only demonstrates the quantum nature of weak values but also presents potential new applications of weak values in analyzing quantum channels and operations.
Measuring the scale parameter of quantum chromodynamics at CHEER
International Nuclear Information System (INIS)
Krauss, L.M.
1981-01-01
The possibility of measuring the scale parameter of quantum chromodynamics, Λsub(s), at CHEER is discussed. Rationale for the measurement of this quantity are given, along with a discussion of the theoretical difficulties involved. The meaurement of the Q 2 dependence of structure functions and their moments, and methods of measuring αsub(s) and its Q 2 evolution, are discussed, and arguments are given for the advantages and disadvantages of going to high Q 2 values at CHEER. It is concluded that while sensitivity to Λ is lowered at high Q 2 , CHEER will, in principle, be able to provide the first clean measurements of Λ, free from almost all the theoretical confusion involved in interpretations of present data
Upper bounds on quantum uncertainty products and complexity measures
Energy Technology Data Exchange (ETDEWEB)
Guerrero, Angel; Sanchez-Moreno, Pablo; Dehesa, Jesus S. [Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Department of Applied Mathematics, University of Granada, Granada (Spain) and Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain); Department of Atomic, Molecular and Nuclear Physics, University of Granada, Granada (Spain); Institute Carlos I for Computational and Theoretical Physics, University of Granada, Granada (Spain)
2011-10-15
The position-momentum Shannon and Renyi uncertainty products of general quantum systems are shown to be bounded not only from below (through the known uncertainty relations), but also from above in terms of the Heisenberg-Kennard product . Moreover, the Cramer-Rao, Fisher-Shannon, and Lopez-Ruiz, Mancini, and Calbet shape measures of complexity (whose lower bounds have been recently found) are also bounded from above. The improvement of these bounds for systems subject to spherically symmetric potentials is also explicitly given. Finally, applications to hydrogenic and oscillator-like systems are done.
Bohr quantum theory of the magnetic monopoles and classical electron electromagnetic mass problem
Pankovic, Vladan
2010-01-01
In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic monopoles theory, especially Dirac electric/magnetic charge quantization condition. It follows after application of Bohr theory at the system, simply called magnetic monopole "atom", consisting of the practically standing, massive magnetic monopole as the "nucleu...
International Nuclear Information System (INIS)
Daoud, M.; Ahl Laamara, R.
2012-01-01
We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states. -- Highlights: ► Pairwise quantum correlations multipartite coherent states. ► Explicit expression of geometric quantum discord. ► Entanglement sudden death and quantum discord robustness. ► Generalized coherent states interpolating between Werner and Greenberger–Horne–Zeilinger states
Energy Technology Data Exchange (ETDEWEB)
Daoud, M., E-mail: m_daoud@hotmail.com [Department of Physics, Faculty of Sciences, University Ibnou Zohr, Agadir (Morocco); Ahl Laamara, R., E-mail: ahllaamara@gmail.com [LPHE-Modeling and Simulation, Faculty of Sciences, University Mohammed V, Rabat (Morocco); Centre of Physics and Mathematics, CPM, CNESTEN, Rabat (Morocco)
2012-07-16
We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states. -- Highlights: ► Pairwise quantum correlations multipartite coherent states. ► Explicit expression of geometric quantum discord. ► Entanglement sudden death and quantum discord robustness. ► Generalized coherent states interpolating between Werner and Greenberger–Horne–Zeilinger states.
Solving Complex Problems: A Convergent Approach to Cognitive Load Measurement
Zheng, Robert; Cook, Anne
2012-01-01
The study challenged the current practices in cognitive load measurement involving complex problem solving by manipulating the presence of pictures in multiple rule-based problem-solving situations and examining the cognitive load resulting from both off-line and online measures associated with complex problem solving. Forty-eight participants…
Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors
Bülte, Johannes; Bednorz, Adam; Bruder, Christoph; Belzig, Wolfgang
2018-04-01
The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.
Baianu, IC
2004-01-01
Two important concepts for nanoscience and nanotechnology-- the quantum automaton and quantum computation--were introduced in the context of quantum genetics and complex genetic networks with nonlinear dynamics. In previous publications (Baianu,1971a, b) the formal definition of quantum automaton was initially presented in the Schrodinger representation of quantum mechanics, and several possible implications for genetic processes and metabolic activities in living cells and organisms were considered. This was followed by reports on quantum, as well as symbolic, abstract computations based on the theory of categories, functors and natural transformations (Baianu,1971b; 1977; 1987; 2004; Baianu et al, 2004). The notions of quantum topological semigroup, quantum automaton, and/or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. A representation of inter...
Quantum theory of multiple-input-multiple-output Markovian feedback with diffusive measurements
International Nuclear Information System (INIS)
Chia, A.; Wiseman, H. M.
2011-01-01
Feedback control engineers have been interested in multiple-input-multiple-output (MIMO) extensions of single-input-single-output (SISO) results of various kinds due to its rich mathematical structure and practical applications. An outstanding problem in quantum feedback control is the extension of the SISO theory of Markovian feedback by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] to multiple inputs and multiple outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow for multiple inputs, multiple outputs, and arbitrary diffusive quantum measurements. We thus obtain a MIMO framework which resembles the SISO theory and whose additional mathematical structure is highlighted by the extensive use of vector-operator algebra.
Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems
Directory of Open Access Journals (Sweden)
Siddharth Muthukrishnan
2016-07-01
Full Text Available Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA, especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final cost function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Finally, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.
Key to good fit: body measurement problems specific to key ...
African Journals Online (AJOL)
Key to good fit: body measurement problems specific to key dimensions. ... to explore and describe the problems that the South African Clothing Industry currently ... A postal survey was conducted among South African apparel and footwear ...
Support of the extremal measure in a vector equilibrium problem
International Nuclear Information System (INIS)
Lapik, M A
2006-01-01
A generalization of the Mhaskar-Saff functional is obtained for a vector equilibrium problem with an external field. As an application, the supports of the equilibrium measures are found in a special vector equilibrium problem with Nikishin matrix.
Using measurement-induced disturbance to characterize correlations as classical or quantum
International Nuclear Information System (INIS)
Luo Shunlong
2008-01-01
In contrast to the seminal entanglement-separability paradigm widely used in quantum information theory, we introduce a quantum-classical dichotomy in order to classify and quantify statistical correlations in bipartite states. This is based on the idea that while in the classical description of nature measurements can be carried out without disturbance, in the quantum description, generic measurements often disturb the system and the disturbance can be exploited to quantify the quantumness of correlations therein. It turns out that certain separable states still possess correlations of a quantum nature and indicates that quantum correlations are more general than entanglement. The results are illustrated in the Werner states and the isotropic states, and are applied to quantify the quantum advantage of the model of quantum computation proposed by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)
Quantum solution to a class of two-party private summation problems
Shi, Run-Hua; Zhang, Shun
2017-09-01
In this paper, we define a class of special two-party private summation (S2PPS) problems and present a common quantum solution to S2PPS problems. Compared to related classical solutions, our solution has advantages of higher security and lower communication complexity, and especially it can ensure the fairness of two parties without the help of a third party. Furthermore, we investigate the practical applications of our proposed S2PPS protocol in many privacy-preserving settings with big data sets, including private similarity decision, anonymous authentication, social networks, secure trade negotiation, secure data mining.
Quantum Entanglement: Separability, Measure, Fidelity of Teleportation, and Distillation
Directory of Open Access Journals (Sweden)
Ming Li
2010-01-01
Full Text Available Quantum entanglement plays crucial roles in quantum information processing. Quantum entangled states have become the key ingredient in the rapidly expanding field of quantum information science. Although the nonclassical nature of entanglement has been recognized for many years, considerable efforts have been taken to understand and characterize its properties recently. In this review, we introduce some recent results in the theory of quantum entanglement. In particular separability criteria based on the Bloch representation, covariance matrix, normal form and entanglement witness, lower bounds, subadditivity property of concurrence and tangle, fully entangled fraction related to the optimal fidelity of quantum teleportation, and entanglement distillation will be discussed in detail.
Do Corruption Measures Have a Perception Problem
DEFF Research Database (Denmark)
Charron, Nicholas
2016-01-01
How well do corruption perception measures reflect actual levels of public sector corruption? Leading cross-national corruption perception measures have come under much theoretical and empirical scrutiny in recent years, with serious implications for the validity and reliability of the data...... in this ever growing sub-field. Critics argue that perceptions – in particular those of outside experts – do not reflect actual corruption in that they are far too ‘noisy’ or simply biased by external factors such as economic performance. Moreover, a number of recent empirical studies, focused on developing...... areas, have put forth evidence that outside expert assessments of corruption correspond little, if at all, with the experiences and views of actual citizens, and that such a lack of correspondence demonstrates pessimism for existing perception measures. This study offers a systematic analysis...
International Nuclear Information System (INIS)
Endo, T.; Murayama, Y.; Sakamoto, Y.; Sakuraba, T.; Shiota, F.
1989-01-01
A series of systems composed of cryogenic devices such as a Josephson potentiometer and a cryogenic current comparator has been proposed and developed to precisely measure a current with any value up to 1 A. These systems will be used to measure the injected electrical energy with an uncertainty of the order of 0.01 ppm or less in the absolute measurement of the magnetic flux quantum by superconducting magnetic levitation. Some preliminary experiments are described
International Nuclear Information System (INIS)
Rae, A.I.M.
1981-01-01
This book, based on a thirty lecture course given to students at the beginning of their second year, covers the quantum mechanics required by physics undergraduates. Early chapters deal with wave mechanics, including a discussion of the energy states of the hydrogen atom. These are followed by a more formal development of the theory, leading to a discussion of some advanced applications and an introduction to the conceptual problems associated with quantum measurement theory. Emphasis is placed on the fundamentals of quantum mechanics. Problems are included at the end of each chapter. (U.K.)
Directory of Open Access Journals (Sweden)
Weidong Lei
2017-01-01
Full Text Available We aim at solving the cyclic scheduling problem with a single robot and flexible processing times in a robotic flow shop, which is a well-known optimization problem in advanced manufacturing systems. The objective of the problem is to find an optimal robot move sequence such that the throughput rate is maximized. We propose a hybrid algorithm based on the Quantum-Inspired Evolutionary Algorithm (QEA and genetic operators for solving the problem. The algorithm integrates three different decoding strategies to convert quantum individuals into robot move sequences. The Q-gate is applied to update the states of Q-bits in each individual. Besides, crossover and mutation operators with adaptive probabilities are used to increase the population diversity. A repairing procedure is proposed to deal with infeasible individuals. Comparison results on both benchmark and randomly generated instances demonstrate that the proposed algorithm is more effective in solving the studied problem in terms of solution quality and computational time.
Generalized flow and determinism in measurement-based quantum computation
Energy Technology Data Exchange (ETDEWEB)
Browne, Daniel E [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Kashefi, Elham [Computing Laboratory and Christ Church College, University of Oxford, Parks Road, Oxford OX1 3QD (United Kingdom); Mhalla, Mehdi [Laboratoire d' Informatique de Grenoble, CNRS - Centre national de la recherche scientifique, Universite de Grenoble (France); Perdrix, Simon [Preuves, Programmes et Systemes (PPS), Universite Paris Diderot, Paris (France)
2007-08-15
We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a necessary and sufficient condition for the stepwise uniformly deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the (X, Y), (X, Z) and (Y, Z) planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the stepwise uniformly deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly valuable for the study of the algorithms and complexity in the one-way model.
Measure theoretical approach to recurrent properties for quantum dynamics
Energy Technology Data Exchange (ETDEWEB)
Otobe, Yoshiki [Department of Mathematical Sciences, Shinshu University, Asahi 3-1-1, Matsumoto 390-8621 (Japan); Sasaki, Itaru, E-mail: otobe@math.shinshu-u.ac.jp, E-mail: isasaki@shinshu-u.ac.jp [Fiber-Nanotech Young Researcher Empowerment Center, Shinshu University, Asahi 3-1-1, Matsumoto 390-8621 (Japan)
2011-11-18
Poincare's recurrence theorem, which states that every Hamiltonian dynamics enclosed in a finite volume returns to its initial position as close as one wishes, is a mathematical basis of statistical mechanics. It is Liouville's theorem that guarantees that the dynamics preserves the volume on the state space. A quantum version of Poincare's theorem was obtained in the middle of the 20th century without any volume structures of the state space (Hilbert space). One of our aims in this paper is to establish such properties of quantum dynamics from an analog of Liouville's theorem, namely, we will construct a natural probability measure on the Hilbert space from a Hamiltonian defined on the space. Then we will show that the measure is invariant under the corresponding Schroedinger flow. Moreover, we show that the dynamics naturally causes an infinite-dimensional Weyl transformation. It also enables us to discuss the ergodic properties of such dynamics. (paper)
Model for calorimetric measurements in an open quantum system
Donvil, Brecht; Muratore-Ginanneschi, Paolo; Pekola, Jukka P.; Schwieger, Kay
2018-05-01
We investigate the experimental setup proposed in New J. Phys. 15, 115006 (2013), 10.1088/1367-2630/15/11/115006 for calorimetric measurements of thermodynamic indicators in an open quantum system. As a theoretical model we consider a periodically driven qubit coupled with a large yet finite electron reservoir, the calorimeter. The calorimeter is initially at equilibrium with an infinite phonon bath. As time elapses, the temperature of the calorimeter varies in consequence of energy exchanges with the qubit and the phonon bath. We show how under weak-coupling assumptions, the evolution of the qubit-calorimeter system can be described by a generalized quantum jump process including as dynamical variable the temperature of the calorimeter. We study the jump process by numeric and analytic methods. Asymptotically with the duration of the drive, the qubit-calorimeter attains a steady state. In this same limit, we use multiscale perturbation theory to derive a Fokker-Planck equation governing the calorimeter temperature distribution. We inquire the properties of the temperature probability distribution close and at the steady state. In particular, we predict the behavior of measurable statistical indicators versus the qubit-calorimeter coupling constant.
Generalized flow and determinism in measurement-based quantum computation
International Nuclear Information System (INIS)
Browne, Daniel E; Kashefi, Elham; Mhalla, Mehdi; Perdrix, Simon
2007-01-01
We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a necessary and sufficient condition for the stepwise uniformly deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the (X, Y), (X, Z) and (Y, Z) planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the stepwise uniformly deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly valuable for the study of the algorithms and complexity in the one-way model
International Nuclear Information System (INIS)
Smith, Kyle K. G.; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J.
2015-01-01
We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics
Entanglement entropy after selective measurements in quantum chains
Energy Technology Data Exchange (ETDEWEB)
Najafi, Khadijeh [Department of Physics, Georgetown University,37th and O Sts. NW, Washington, DC 20057 (United States); Rajabpour, M.A. [Instituto de Física, Universidade Federal Fluminense,Av. Gal. Milton Tavares de Souza s/n, Gragoatá, 24210-346, Niterói, RJ (Brazil)
2016-12-22
We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.
Entanglement entropy after selective measurements in quantum chains
International Nuclear Information System (INIS)
Najafi, Khadijeh; Rajabpour, M.A.
2016-01-01
We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.
Directory of Open Access Journals (Sweden)
Francisco Savall Alemany
2017-01-01
Full Text Available The effectiveness of the problem based teaching on the science learning has been highlighted by the didactic research. This teaching model is characterized by organizing the units around problems and by proposing a research plan to find a solution which requires concepts and models to be introduced in a functional way, as possible solutions to the problem. In this article we present a problem based unit for teaching quantum physics in introductory physics courses and we analyze in detail the teaching strategy that we follow to build a model to explain the emission and absorption of radiation.
Directory of Open Access Journals (Sweden)
Bruno Avila Leal de Meirelles Herrera
2015-12-01
Full Text Available ABSTRACT The Traveling Salesman Problem (TSP is one of the most well-known and studied problems of Operations Research field, more specifically, in the Combinatorial Optimization field. As the TSP is a NP (Non-Deterministic Polynomial time-hard problem, there are several heuristic methods which have been proposed for the past decades in the attempt to solve it the best possible way. The aim of this work is to introduce and to evaluate the performance of some approaches for achieving optimal solution considering some symmetrical and asymmetrical TSP instances, which were taken from the Traveling Salesman Problem Library (TSPLIB. The analyzed approaches were divided into three methods: (i Lin-Kernighan-Helsgaun (LKH algorithm; (ii LKH with initial tour based on uniform distribution; and (iii an hybrid proposal combining Particle Swarm Optimization (PSO with quantum inspired behavior and LKH for local search procedure. The tested algorithms presented promising results in terms of computational cost and solution quality.
Holographic multiverse and the measure problem
Energy Technology Data Exchange (ETDEWEB)
Vilenkin, Alexander, E-mail: vilenkin@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2011-06-01
We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation between the UV cutoff scale ξ on the boundary and the hypersurface Σ on which the wave function is defined in the bulk. We propose that in the limit ξ → 0 this hypersurface should be used as the cutoff surface in the multiverse measure. Furthermore, we argue that in the inflating regions of spacetime with a slowly varying Hubble rate H the hypersurfaces Σ are surfaces of constant comoving apparent horizon (CAH). Finally, we introduce a measure prescription (called CAH+) which appears to have no pathological features and coincides with the constant CAH cutoff in regions of slowly varying H.
Holographic multiverse and the measure problem
International Nuclear Information System (INIS)
Vilenkin, Alexander
2011-01-01
We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation between the UV cutoff scale ξ on the boundary and the hypersurface Σ on which the wave function is defined in the bulk. We propose that in the limit ξ → 0 this hypersurface should be used as the cutoff surface in the multiverse measure. Furthermore, we argue that in the inflating regions of spacetime with a slowly varying Hubble rate H the hypersurfaces Σ are surfaces of constant comoving apparent horizon (CAH). Finally, we introduce a measure prescription (called CAH+) which appears to have no pathological features and coincides with the constant CAH cutoff in regions of slowly varying H
Understanding quantum mechanics by measuring the properties of mesoscopic devices
International Nuclear Information System (INIS)
Webb, R.
1993-01-01
Measurements of the electrical transport and magnetic properties of micron-size scale insulators, metals, semi-metals, and semiconductors at low temperatures have uncovered a wealth of unexpected phenomena. The only way to understand these new properties is by invoking many of the postulates of quantum mechanics. The author has confirmed that the electron acts as a long-range phase-coherent wave and conventional classical forces are not as important as scalar and vector potentials in determining the response of the electron as it moves through its environment. This talk will focus on the measurement of the Aharonov-Bohm self-interference effects, nonlocal transport phenomena, and persistent currents in normal metal ring structures that have been observed in these nanostructures
Reality, measurement and locality in Quantum Field Theory
International Nuclear Information System (INIS)
Tommasini, Daniele
2002-01-01
It is currently believed that the local causality of Quantum Field Theory (QFT) is destroyed by the measurement process. This belief is also based on the Einstein-Podolsky-Rosen (EPR) paradox and on the so-called Bell's theorem, that are thought to prove the existence of a mysterious, instantaneous action between distant measurements. However, I have shown recently that the EPR argument is removed, in an interpretation-independent way, by taking into account the fact that the Standard Model of Particle Physics prevents the production of entangled states with a definite number of particles. This result is used here to argue in favor of a statistical interpretation of QFT and to show that it allows for a full reconciliation with locality and causality. Within such an interpretation, as Ballentine and Jarret pointed out long ago, Bell's theorem does not demonstrate any nonlocality. (author)
Admittance measurements in the quantum Hall effect regime
Energy Technology Data Exchange (ETDEWEB)
Hernández, C., E-mail: carlos.hernandezr@unimilitar.edu.co [Departamento de Física, Universidad Militar Nueva Granada, Carrera 11 # 101-80, Bogotá D.C. (Colombia); Laboratorio de Magnetismo, Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá D.C. (Colombia); Consejo, C.; Chaubet, C. [Laboratoire Charles Coulomb L2C, Université Montpellier II, Pl. E. Bataillon, 34095 Montpellier Cedex 5 (France)
2014-11-15
In this work we present an admittance study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. We have studied several Hall bars in different contacts configurations in the frequency range 100 Hz–1 MHz. Our interpretation is based on the Landauer–Büttiker theory and takes into account both the capacitance and the topology of the coaxial cables which are connected to the sample holder. We show that we always observe losses through the capacitive impedance of the coaxial cables, except in the two contacts configuration in which the cable capacitance does not influence the admittance measurement of the sample. In this case, we measure the electrochemical capacitance of the 2DEG and show its dependence with the filling factor ν.
Decoherence bypass of macroscopic superpositions in quantum measurement
International Nuclear Information System (INIS)
Spehner, Dominique; Haake, Fritz
2008-01-01
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object-pointer entanglement and environment-induced decoherence of distinct pointer readouts to proceed simultaneously, such that mixtures of macroscopically distinct object-pointer product states arise without intervening macroscopic superpositions, and (iii) go beyond the Markovian treatment of decoherence. (fast track communication)
Problems in determining the optimal use of road safety measures
DEFF Research Database (Denmark)
Elvik, Rune
2014-01-01
for intervention that ensures maximum safety benefits. The third problem is how to develop policy options to minimise the risk of indivisibilities and irreversible choices. The fourth problem is how to account for interaction effects between road safety measures when determining their optimal use. The fifth......This paper discusses some problems in determining the optimal use of road safety measures. The first of these problems is how best to define the baseline option, i.e. what will happen if no new safety measures are introduced. The second problem concerns choice of a method for selection of targets...... problem is how to obtain the best mix of short-term and long-term measures in a safety programme. The sixth problem is how fixed parameters for analysis, including the monetary valuation of road safety, influence the results of analyses. It is concluded that it is at present not possible to determine...
Quantum Measurements: From Bayes Rule to Neural Networks
DEFF Research Database (Denmark)
Greplova, Eliska
2017-01-01
Quantum technologies are becoming more and more introduced into the devices that we use in the daily life, such as quantum dot based television screens or quantum cryptographic channels for encoding financial transactions. Given the limits of the silicon computer chips, it will in the near future...... learning techniques such as artificial neural networks....
Control-free control: Manipulating a quantum system using only a limited set of measurements
International Nuclear Information System (INIS)
Ashhab, S.; Nori, Franco
2010-01-01
We present and discuss different protocols for preparing an arbitrary quantum state of a qubit using only a restricted set of measurements, with no unitary operations at all. We show that an arbitrary state can indeed be prepared, provided that the available measurements satisfy certain requirements. Our results shed light on the role that measurement-induced back-action plays in quantum feedback control and the extent to which this back-action can be exploited in quantum-control protocols.
Convergence of repeated quantum nondemolition measurements and wave-function collapse
International Nuclear Information System (INIS)
Bauer, Michel; Bernard, Denis
2011-01-01
Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.
Statistical and stochastic aspects of the delocalization problem in quantum mechanics
International Nuclear Information System (INIS)
Claverie, P.; Diner, S.
1976-01-01
The space-time behaviour of electrons in atoms and molecules is reviewed. The wave conception of the electron is criticized and the poverty of the non-reductionist attitude is underlined. Further, the two main interpretations of quantum mechanics are recalled: the Copenhagen and the Statistical Interpretations. The meaning and the successes of the Statistical Interpretation are explained and it is shown that it does not solve all problems because quantum mechanics is irreducible to a classical statistical theory. The fluctuation of the particle number and its relationship to loge theory, delocalization and correlation is studied. Finally, different stochastic models for microphysics are reviewed. The markovian Fenyes-Nelson process allows an interpretation of the original heuristic considerations of Schroedinger. Non-markov processes with Schroedinger time evolution are shown to be equivalent to the base state analysis of Feynmann but they are unsatisfactory from a probabilistic point of view. Stochastic electrodynamics is presented as the most satisfactory conception nowadays
Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures
Sharma, Kunal; Das, Tamoghna; Sen (de), Aditi; Sen, Ujjwal
Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamybased multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.
Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals.
Miao, Haixing; Adhikari, Rana X; Ma, Yiqiu; Pang, Belinda; Chen, Yanbei
2017-08-04
The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.
Collapsing a perfect superposition to a chosen quantum state without measurement.
Directory of Open Access Journals (Sweden)
Ahmed Younes
Full Text Available Given a perfect superposition of [Formula: see text] states on a quantum system of [Formula: see text] qubits. We propose a fast quantum algorithm for collapsing the perfect superposition to a chosen quantum state [Formula: see text] without applying any measurements. The basic idea is to use a phase destruction mechanism. Two operators are used, the first operator applies a phase shift and a temporary entanglement to mark [Formula: see text] in the superposition, and the second operator applies selective phase shifts on the states in the superposition according to their Hamming distance with [Formula: see text]. The generated state can be used as an excellent input state for testing quantum memories and linear optics quantum computers. We make no assumptions about the used operators and applied quantum gates, but our result implies that for this purpose the number of qubits in the quantum register offers no advantage, in principle, over the obvious measurement-based feedback protocol.
An approach using quantum ant colony optimization applied to the problem of nuclear reactors reload
International Nuclear Information System (INIS)
Silva, Marcio H.; Lima, Alan M.M. de; Schirru, Roberto; Medeiros, J.A.C.C.
2009-01-01
The basic concept behind the nuclear reactor fuel reloading problem is to find a configuration of new and used fuel elements, to keep the plant working at full power by the largest possible duration, within the safety restrictions. The main restriction is the power peaking factor, which is the limit value for the preservation of the fuel assembly. The QACO A lfa algorithm is a modified version of Quantum Ant Colony Optimization (QACO) proposed by Wang et al, which uses a new actualization method and a pseudo evaporation step. We examined the QACO A lfa behavior associated to physics of reactors code RECNOD when applied to this problem. Although the QACO have been developed for continuous functions, the binary model used in this work allows applying it to discrete problems, such as the mentioned above. (author)
Pedagogical Review of Quantum Measurement Theory with an Emphasis on Weak Measurements
Directory of Open Access Journals (Sweden)
Bengt E. Y. Svensson
2013-05-01
Full Text Available The quantum theory of measurement has been with us since quantum mechanics was invented. It has recently been invigorated, partly due to the increasing interest in quantum information science. In this partly pedagogical review I attempt to give a self-contained overview of non-relativistic quantum theory of measurement expressed in density matrix formalism. I will not dwell on the applications in quantum information theory; it is well covered by several books in that field. The focus is instead on applications to the theory of weak measurement, as developed by Aharonov and collaborators. Their development of weak measurement combined with what they call post-selection - judiciously choosing not only the initial state of a system (pre-selection but also its final state - has received much attention recently. Not the least has it opened up new, fruitful experimental vistas, like novel approaches to amplification. But the approach has also attached to it some air of mystery. I will attempt to demystify it by showing that (almost all results can be derived in a straight-forward way from conventional quantum mechanics. Among other things, I develop the formalism not only to first order but also to second order in the weak interaction responsible for the measurement. I apply it to the so called Leggett-Garg inequalities, also known as Bell inequalities in time. I also give an outline, even if rough, of some of the ingenious experiments that the work by Aharonov and collaborators has inspired. As an application of weak measurement, not related to the approach by Aharonov and collaborators, the formalism also allows me to derive the master equation for the density matrix of an open system in interaction with an environment. An issue that remains in the weak measurement plus post-selection approach is the interpretation of the so called weak value of an observable. Is it a bona fide property of the system considered? I have no definite answer to this
Novel Schemes for Measurement-Based Quantum Computation
International Nuclear Information System (INIS)
Gross, D.; Eisert, J.
2007-01-01
We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique develops tools from many-body physics--based on finitely correlated or projected entangled pair states--to go beyond the cluster-state based one-way computer. We identify resource states radically different from the cluster state, in that they exhibit nonvanishing correlations, can be prepared using nonmaximally entangling gates, or have very different local entanglement properties. In the computational models, randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. We comment on the possibility of tailoring computational models to specific physical systems
Novel schemes for measurement-based quantum computation.
Gross, D; Eisert, J
2007-06-01
We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique develops tools from many-body physics-based on finitely correlated or projected entangled pair states-to go beyond the cluster-state based one-way computer. We identify resource states radically different from the cluster state, in that they exhibit nonvanishing correlations, can be prepared using nonmaximally entangling gates, or have very different local entanglement properties. In the computational models, randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. We comment on the possibility of tailoring computational models to specific physical systems.
One-sided measurement-device-independent quantum key distribution
Cao, Wen-Fei; Zhen, Yi-Zheng; Zheng, Yu-Lin; Li, Li; Chen, Zeng-Bing; Liu, Nai-Le; Chen, Kai
2018-01-01
Measurement-device-independent quantum key distribution (MDI-QKD) protocol was proposed to remove all the detector side channel attacks, while its security relies on the trusted encoding systems. Here we propose a one-sided MDI-QKD (1SMDI-QKD) protocol, which enjoys detection loophole-free advantage, and at the same time weakens the state preparation assumption in MDI-QKD. The 1SMDI-QKD can be regarded as a modified MDI-QKD, in which Bob's encoding system is trusted, while Alice's is uncharacterized. For the practical implementation, we also provide a scheme by utilizing coherent light source with an analytical two decoy state estimation method. Simulation with realistic experimental parameters shows that the protocol has a promising performance, and thus can be applied to practical QKD applications.
Energy Technology Data Exchange (ETDEWEB)
Messer, Joachim August
2007-07-01
Quantum mechanics in the conception, as it is today present, contains - what concerns its conceivable understanding and its interpretation - numerous paradoxa. The best known Copenhagen interpretation is critized and other interpretations, as the many-world interpretation and the modern, today mostly attended decoherence interpretation are put to this describingly on side. Axiomatic explanation attempts, like those from Mackey, Jauch, and Piron are analyzed and the measurement problem discussed from three ways of view: the introduction of a cut by Georg Suessmann, the scaling formalism from Klaus Hepp, and the philosophy from Bernulf Kanitschneider. Especially the critique given by Albert Einstein on the Bohr-Heisenberg Copenhagen interpretation and the completeness of a realistic quantum theory by the EPR thought experiment (called from Einstein, Podolsky, and Rosen) is more detailedly studied and extended to a holomorphic realism, in which the measurement quantities become visible as boundary values of a holomorphic function. This analytic continuation throws a new light on the body-soul parallelism, which exceeds the positions of Platon and Feigl. Beside the decoherence also the superselection rules, which are extensively discussed, are an example for a realistic state reduction - however the nonlocality of realistic quantum mechanics forces to a dualism of Higgs' symmetry breaking with local decoherence in the terrestrial laboratory. The position of a holomorphic barycentric realism is worked out by regress to the quantum field theory of Lehmann, Symanzik, and Zimmermann (LSZ) with its reduction formula. Quantum-cosmological implications, non-commutative geometry, K theory, and background field are also discussed. The newly designed knowledge theory of the holomorphic, barycentric realism - which in the classical limit goes over in a critical realism - forms also a bridge to a deepened humanism, which cannot be constructed from purely classical physics. As
Energy Technology Data Exchange (ETDEWEB)
Messer, Joachim August
2007-07-01
Quantum mechanics in the conception, as it is today present, contains - what concerns its conceivable understanding and its interpretation - numerous paradoxa. The best known Copenhagen interpretation is critized and other interpretations, as the many-world interpretation and the modern, today mostly attended decoherence interpretation are put to this describingly on side. Axiomatic explanation attempts, like those from Mackey, Jauch, and Piron are analyzed and the measurement problem discussed from three ways of view: the introduction of a cut by Georg Suessmann, the scaling formalism from Klaus Hepp, and the philosophy from Bernulf Kanitschneider. Especially the critique given by Albert Einstein on the Bohr-Heisenberg Copenhagen interpretation and the completeness of a realistic quantum theory by the EPR thought experiment (called from Einstein, Podolsky, and Rosen) is more detailedly studied and extended to a holomorphic realism, in which the measurement quantities become visible as boundary values of a holomorphic function. This analytic continuation throws a new light on the body-soul parallelism, which exceeds the positions of Platon and Feigl. Beside the decoherence also the superselection rules, which are extensively discussed, are an example for a realistic state reduction - however the nonlocality of realistic quantum mechanics forces to a dualism of Higgs' symmetry breaking with local decoherence in the terrestrial laboratory. The position of a holomorphic barycentric realism is worked out by regress to the quantum field theory of Lehmann, Symanzik, and Zimmermann (LSZ) with its reduction formula. Quantum-cosmological implications, non-commutative geometry, K theory, and background field are also discussed. The newly designed knowledge theory of the holomorphic, barycentric realism - which in the classical limit goes over in a critical realism - forms also a bridge to a deepened humanism, which cannot be constructed from purely classical physics. As
Solution of relativistic quantum optics problems using clusters of graphical processing units
Energy Technology Data Exchange (ETDEWEB)
Gordon, D.F., E-mail: daviel.gordon@nrl.navy.mil; Hafizi, B.; Helle, M.H.
2014-06-15
Numerical solution of relativistic quantum optics problems requires high performance computing due to the rapid oscillations in a relativistic wavefunction. Clusters of graphical processing units are used to accelerate the computation of a time dependent relativistic wavefunction in an arbitrary external potential. The stationary states in a Coulomb potential and uniform magnetic field are determined analytically and numerically, so that they can used as initial conditions in fully time dependent calculations. Relativistic energy levels in extreme magnetic fields are recovered as a means of validation. The relativistic ionization rate is computed for an ion illuminated by a laser field near the usual barrier suppression threshold, and the ionizing wavefunction is displayed.
Transitions in the computational power of thermal states for measurement-based quantum computation
International Nuclear Information System (INIS)
Barrett, Sean D.; Bartlett, Stephen D.; Jennings, David; Doherty, Andrew C.; Rudolph, Terry
2009-01-01
We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct 'phases' - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical, or quantum in the underlying spin-lattice model.
Quantum optical arbitrary waveform manipulation and measurement in real time.
Kowligy, Abijith S; Manurkar, Paritosh; Corzo, Neil V; Velev, Vesselin G; Silver, Michael; Scott, Ryan P; Yoo, S J B; Kumar, Prem; Kanter, Gregory S; Huang, Yu-Ping
2014-11-17
We describe a technique for dynamic quantum optical arbitrary-waveform generation and manipulation, which is capable of mode selectively operating on quantum signals without inducing significant loss or decoherence. It is built upon combining the developed tools of quantum frequency conversion and optical arbitrary waveform generation. Considering realistic parameters, we propose and analyze applications such as programmable reshaping of picosecond-scale temporal modes, selective frequency conversion of any one or superposition of those modes, and mode-resolved photon counting. We also report on experimental progress to distinguish two overlapping, orthogonal temporal modes, demonstrating over 8 dB extinction between picosecond-scale time-frequency modes, which agrees well with our theory. Our theoretical and experimental progress, as a whole, points to an enabling optical technique for various applications such as ultradense quantum coding, unity-efficiency cavity-atom quantum memories, and high-speed quantum computing.
Problems of provision of unity of measurements in medicine
International Nuclear Information System (INIS)
Tarbeev, Yu.V.
1998-01-01
The problems on providing the measurement unity in medicine on the country scale and within the world community frames are considered. Attention is paid to thermometry, pressure and viscosity measurements, studies in the area of colour vision and laser technique, electrometry, magnetic fields parameters measurements and physico-chemical measurements. The main accent is made on ionizing radiation metrology. The problems on metrological provision of intellectual measurement means for medical purposes and the reference base of Russia as the basis for providing the measurement unity in medicine are also discussed [ru
Classicality in quantum mechanics
International Nuclear Information System (INIS)
Dreyer, Olaf
2007-01-01
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity
Classicality in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Dreyer, Olaf [Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ (United Kingdom)
2007-05-15
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity.
The informationally-complete quantum theory
Chen, Zeng-Bing
2014-01-01
Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum mechanics. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here we present an informationally-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that ...
Energy Technology Data Exchange (ETDEWEB)
Azevedo, G.; Monte, A. F. G.; Reis, A. F.; Messias, D. N. [Laboratório de Espectroscopia Óptica, Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, MG 38400-902 (Brazil)
2014-11-17
The study of the spatial photon migration as a function of the concentration brings into attention the problem of the energy transfer in quantum dot embedded systems. By measuring the photon propagation and its spatial dependence, it is possible to understand the whole dynamics in a quantum dot system, and also improve their concentration dependence to maximize energy propagation due to radiative and non-radiative processes. In this work, a confocal microscope was adapted to scan the spatial distribution of photoluminescence from CdSe-ZnS core-shell quantum dots in colloidal solutions. The energy migration between the quantum dots was monitored by the direct measurement of the photon diffusion length, according to the diffusion theory. We observed that the photon migration length decreases by increasing the quantum dot concentration, this kind of behavior has been regarded as a signature of Förster resonance energy transfer in the system.
Design of coherent quantum observers for linear quantum systems
International Nuclear Information System (INIS)
Vuglar, Shanon L; Amini, Hadis
2014-01-01
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum H ∞ optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs. (paper)
Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets
International Nuclear Information System (INIS)
Aquilanti, Vincenzo; Tonzani, Stefano
2004-01-01
Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known 'symmetric' and 'asymmetric' parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems
Stochastic mechanics and the Kepler problem: Diffusions generated by the quantum motion
International Nuclear Information System (INIS)
Garbaczewski, P.
1986-01-01
We construct a class of solutions of the Schroedinger equation for the Coulomb-Kepler problem. Their ψ = ρ 1/2 exp(iS/ℎ) structure implies that the quantal dynamics of wave functions is completely determined by the related classical Hamiltonian system. A construction of the associated controlled stochastic processes is then possible, their drift velocity being entirely defined in terms of (explicitly known) probability density ρ(x,y,z,t) and phase S(x,y,z,t). In particular, for the stationary states of the quantum problem, in its four-oscillator reconstruction, we identify the regime in which the related classical Hamiltonian can be effectively replaced by the Hamiltonian of the classical Kepler motion. (orig.)
A critical analysis of the quantum theory of measurement
International Nuclear Information System (INIS)
Fer, F.
1984-01-01
Keeping strictly in the positivist and probabilistic, hence hilbertian frame of Quantum Mechanics, the author tries to ascertain whether or not Quantum Mechanics, starting from its axioms, reaches the aim of any physical theory, that is, comparison with experiment. The answer is: no, as long as it keeps close to the existing axiomatics, and also to accurate mathematics. (Auth.)
Mean values and measures in quantum mechanics and classical mechanics
International Nuclear Information System (INIS)
Bass, J.
1980-01-01
In quantum mechanics, for a system at a fixed time, the theory of operators associates to every physical quantity X a probability law. But it is not possible to associate a probability law to a pair (X, Y) of operators, when they do not commute. Therefore it is not possible to represent the physical quantities by the usual methods of probability theory. The aim of this paper is to show that, if X, Y are represented by non random functions which are oscillating in such a way that they generate temporal averages their exist pairs of functions X, Y which have properties similar to pairs of operators. To X and to Y it is possible to associate two measures analogous to probability measures, but that is not possible for the pair (X, Y). The functions satisfying to such conditions are the pseudo-random function, a class of stationary functions which is complementary of the class of almost-periodic functions. The construction of these functions makes use of uniformly distributed sequences of real numbers, which constitute a simulation of random variables uniformly distributed over [0, 1]. Their properties are consequences of the ergodic theorems of H. Weyl (1916) and are related to the properties of irrational numbers [fr
Fast automotive diesel exhaust measurement using quantum cascade lasers
Herbst, J.; Brunner, R.; Lambrecht, A.
2013-12-01
Step by step, US and European legislations enforce the further reduction of atmospheric pollution caused by automotive exhaust emissions. This is pushing automotive development worldwide. Fuel efficient diesel engines with SCRtechnology can impede NO2-emission by reduction with NH3 down to the ppm range. To meet the very low emission limits of the Euro6 resp. US NLEV (National Low Emission Vehicle) regulations, automotive manufacturers have to optimize continuously all phases of engine operation and corresponding catalytic converters. Especially nonstationary operation holds a high potential for optimizing gasoline consumption and further reducing of pollutant emissions. Test equipment has to cope with demanding sensitivity and speed requirements. In the past Fraunhofer IPM has developed a fast emission analyzer called DEGAS (Dynamic Exhaust Gas Analyzer System), based on cryogenically cooled lead salt lasers. These systems have been used at Volkswagen AG`s test benches for a decade. Recently, IPM has developed DEGAS-Next which is based on cw quantum cascade lasers and thermoelectrically cooled detectors. The system is capable to measure three gas components (i.e. NO, NO2, NH3) in two channels with a time resolution of 20 ms and 1 ppm detection limits. We shall present test data and a comparison with fast FTIR measurements.
International Nuclear Information System (INIS)
Eriksson, Karl-Erik
2009-01-01
The measurement process of quantum mechanics is analysed in the scattering theory of quantum field theory. A matrix of bilinear forms of the scattering amplitudes (the R-matrix) is used as the basic descriptive tool. The measurement process is viewed as a final-state interaction described through a series of linear stochastic mappings of the R-matrix, not changing the observable to be measured. The unknown details of the measurement apparatus enter through the stochasticity of the mappings. Although linear in terms of the R-matrix, the mappings are nonlinear in the density matrix, which is obtainable from the R-matrix through normalization. The eigenstates of the observable are the attractors of the mapping process. This result, known from previous generalizations of quantum mechanics, is obtained here within linear quantum mechanics. The conclusion is that the measurement process can be understood within relativistic quantum field theory itself without any generalization or metatheory.
The Problem of the Instrument Stabilization During Hydrographic Measurements
Directory of Open Access Journals (Sweden)
Felski Andrzej
2016-06-01
Full Text Available Performing any measurement on watercraft is connected with many additional difficulties caused by the sea-environment. The most important is the problem of spatial stabilization of measurement systems, which are usually fastened to craft body. As soon as usually these measurement are executed during the move of the craft additional question is the accuracy of execution the planed trajectory.
Measuring Problem Solving Skills in Plants vs. Zombies 2
Shute, Valerie J.; Moore, Gregory R.; Wang, Lubin
2015-01-01
We are using stealth assessment, embedded in "Plants vs. Zombies 2," to measure middle-school students' problem solving skills. This project started by developing a problem solving competency model based on a thorough review of the literature. Next, we identified relevant in-game indicators that would provide evidence about students'…
Quantum ensembles of quantum classifiers.
Schuld, Maria; Petruccione, Francesco
2018-02-09
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
The measurement problem on classical diffusion process: inverse method on stochastic processes
International Nuclear Information System (INIS)
Bigerelle, M.; Iost, A.
2004-01-01
In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time-distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement
Zhou, Hua; Su, Yang; Wang, Rong; Zhu, Yong; Shen, Huiping; Pu, Tao; Wu, Chuanxin; Zhao, Jiyong; Zhang, Baofu; Xu, Zhiyong
2017-10-01
Online reconstruction of a time-variant quantum state from the encoding/decoding results of quantum communication is addressed by developing a method of evolution reconstruction from a single measurement record with random time intervals. A time-variant two-dimensional state is reconstructed on the basis of recovering its expectation value functions of three nonorthogonal projectors from a random single measurement record, which is composed from the discarded qubits of the six-state protocol. The simulated results prove that our method is robust to typical metro quantum channels. Our work extends the Fourier-based method of evolution reconstruction from the version for a regular single measurement record with equal time intervals to a unified one, which can be applied to arbitrary single measurement records. The proposed protocol of evolution reconstruction runs concurrently with the one of quantum communication, which can facilitate the online quantum tomography.
International Nuclear Information System (INIS)
Xiang Guo-Yong; Guo Guang-Can
2013-01-01
The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts: measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters (e.g., squeezed state and quantum entanglement) yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are. (topical review - quantum information)
Solving a Higgs optimization problem with quantum annealing for machine learning.
Mott, Alex; Job, Joshua; Vlimant, Jean-Roch; Lidar, Daniel; Spiropulu, Maria
2017-10-18
The discovery of Higgs-boson decays in a background of standard-model processes was assisted by machine learning methods. The classifiers used to separate signals such as these from background are trained using highly unerring but not completely perfect simulations of the physical processes involved, often resulting in incorrect labelling of background processes or signals (label noise) and systematic errors. Here we use quantum and classical annealing (probabilistic techniques for approximating the global maximum or minimum of a given function) to solve a Higgs-signal-versus-background machine learning optimization problem, mapped to a problem of finding the ground state of a corresponding Ising spin model. We build a set of weak classifiers based on the kinematic observables of the Higgs decay photons, which we then use to construct a strong classifier. This strong classifier is highly resilient against overtraining and against errors in the correlations of the physical observables in the training data. We show that the resulting quantum and classical annealing-based classifier systems perform comparably to the state-of-the-art machine learning methods that are currently used in particle physics. However, in contrast to these methods, the annealing-based classifiers are simple functions of directly interpretable experimental parameters with clear physical meaning. The annealer-trained classifiers use the excited states in the vicinity of the ground state and demonstrate some advantage over traditional machine learning methods for small training datasets. Given the relative simplicity of the algorithm and its robustness to error, this technique may find application in other areas of experimental particle physics, such as real-time decision making in event-selection problems and classification in neutrino physics.
An integrity measure to benchmark quantum error correcting memories
Xu, Xiaosi; de Beaudrap, Niel; O'Gorman, Joe; Benjamin, Simon C.
2018-02-01
Rapidly developing experiments across multiple platforms now aim to realise small quantum codes, and so demonstrate a memory within which a logical qubit can be protected from noise. There is a need to benchmark the achievements in these diverse systems, and to compare the inherent power of the codes they rely upon. We describe a recently introduced performance measure called integrity, which relates to the probability that an ideal agent will successfully ‘guess’ the state of a logical qubit after a period of storage in the memory. Integrity is straightforward to evaluate experimentally without state tomography and it can be related to various established metrics such as the logical fidelity and the pseudo-threshold. We offer a set of experimental milestones that are steps towards demonstrating unconditionally superior encoded memories. Using intensive numerical simulations we compare memories based on the five-qubit code, the seven-qubit Steane code, and a nine-qubit code which is the smallest instance of a surface code; we assess both the simple and fault-tolerant implementations of each. While the ‘best’ code upon which to base a memory does vary according to the nature and severity of the noise, nevertheless certain trends emerge.
Electromagnetic and quantum measurements a bitemporal neoclassical theory
Wessel-Berg, Tore
2001-01-01
It is a pleasure to write a foreword for Professor Tore Wessel-Berg's book, "Electromagnetic and Quantum Measurements: A Bitemporal Neoclassical Theory." This book appeals to me for several reasons. The most important is that, in this book, Wessel-Berg breaks from the pack. The distinguished astrophysicist Thomas Gold has written about the pressures on scientists to move in tight formation, to avoid having their legs nipped by the sheepdogs of science. This book demonstrates that Wessel-Berg is willing to take that risk. I confess that I do not sufficiently understand this book to be able to either agree or disagree with its thesis. Nevertheless, Wessel-Berg makes very cogent arguments for setting out on his journey. The basic equations of physics are indeed time-reversible. Our experience, that leads us to the concept of an "arrow of time," is derived from macro scopic phenomena, not from fundamental microscopic phenomena. For this reason, it makes very good sense to explore the consequences of treating mi...
Inhibited quantum processes through repeated measurements: An approach to quantum zero effect?
International Nuclear Information System (INIS)
Crespo, G.; Proto, A.N.; Cerdeira, H.A.
1992-04-01
The dynamics of a finite set of relevant observables, associated to a Hamiltonian of a three level system is analyzed in connection with the quantum Zeno effect. Since we use the Hamiltonian that completely describes the physical situation related to the experiment under study (W.M. Itano et al, Phys. Rev. A41, 2295 (1990)), no reduction or collapse of the wave function is required to describe the quantum Zeno effect. (author). 18 refs, 18 figs
International Nuclear Information System (INIS)
Zanzi, Andrea
2010-01-01
The chameleonic behavior of the string theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the nonequivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct dark energy scale is recovered in the Einstein frame (E-frame) without unnatural fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e., the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points.
Nucleon many-body problem using quantum-mechanical few-body technique
International Nuclear Information System (INIS)
Horiuchi, Wataru
2016-01-01
A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)
Quantum to Classical Transitions via Weak Measurements and Post-Selection
Cohen, Eliahu; Aharonov, Yakir
Alongside its immense empirical success, the quantum mechanical account of physical systems imposes a myriad of divergences from our thoroughly ingrained classical ways of thinking. These divergences, while striking, would have been acceptable if only a continuous transition to the classical domain was at hand. Strangely, this is not quite the case. The difficulties involved in reconciling the quantum with the classical have given rise to different interpretations, each with its own shortcomings. Traditionally, the two domains are sewed together by invoking an ad hoc theory of measurement, which has been incorporated in the axiomatic foundations of quantum theory. This work will incorporate a few related tools for addressing the above conceptual difficulties: deterministic operators, weak measurements, and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it onto an eigenstate of the measured observable. A single weak measurement yieldsan almost random outcome, but when performed repeatedly over a large ensemble, the averaged outcome becomes increasingly robust and accurate. Importantly, a long sequence of weak measurements can be thought of as a single projective measurement. We claim in this work that classical variables appearing in the o-world, such as center of mass, moment of inertia, pressure, and average forces, result from a multitude of quantum weak measurements performed in the micro-world. Here again, the quantum outcomes are highly uncertain, but the law of large numbers obliges their convergence to the definite quantities we know from our everyday lives. By augmenting this description with a final boundary condition and employing the notion of "classical
International Nuclear Information System (INIS)
Carbo, R.; Calabuig, B.
1988-01-01
Molecular similarity measures within the quantum concept of density functions are described and analyzed. It is intended to show how artificial intelligence techniques can be used within the framework of quantum theory, in order to study and classify the molecular structures and their properties. (A.C.A.S) [pt
International Nuclear Information System (INIS)
Sen, S.; Roy Chowdhury, A.
1989-06-01
The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs
Controlling the sign problem in finite-density quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Garron, Nicolas; Langfeld, Kurt [University of Liverpool, Theoretical Physics Division, Department of Mathematical Sciences, Liverpool (United Kingdom)
2017-07-15
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the ''telegraphic'' approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign-problem regime. (orig.)
The quantum-field renormalization group in the problem of a growing phase boundary
International Nuclear Information System (INIS)
Antonov, N.V.; Vasil'ev, A.N.
1995-01-01
Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab
Controlling the sign problem in finite-density quantum field theory
Garron, Nicolas; Langfeld, Kurt
2017-07-01
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.
Polar optical phonons in a semiconductor quantum-well: The complete matching problem
International Nuclear Information System (INIS)
Nieto, J.M.; Comas, F.
2007-01-01
Confined polar optical phonons in a semiconductor quantum-well (QW) are studied by applying a phenomenological theory which was proposed a few years ago and is based on a continuum approach. This theory considers the coupled character of the electromechanical vibrations and takes due account of both the electric and mechanical boundary conditions. In the present work, we have applied the so-called complete matching problem in contrast with all previous published works on the subject, where more restrictive approximate boundary conditions has been applied. We also consider the effects of strains at the interfaces on the phonon spectra. Comparisons with previous works are made, while we focused on the study of a ZnTe/CdTe/ZnTe QW
Coping with the node problem in quantum hydrodynamics: The covering function method
International Nuclear Information System (INIS)
Babyuk, Dmytro; Wyatt, Robert E.
2004-01-01
A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet
A Numerical Approach to Optimal Coherent Quantum LQG Controller Design Using Gradient Descent
Sichani, Arash Kh.; Vladimirov, Igor G.; Petersen, Ian R.
2016-01-01
This paper is concerned with coherent quantum linear quadratic Gaussian (CQLQG) control. The problem is to find a stabilizing measurement-free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed-loop system. The plant and controller are open quantum systems interconnected through bosonic quantum fields. In comparison with the observation-actuation structure of classical controllers, coherent quantum feedback is less invasive to the quantum ...
Directory of Open Access Journals (Sweden)
Jingling Zhang
2012-01-01
Full Text Available The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self-adaptive grid multi-objective quantum evolutionary algorithm (MOQEA for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due-time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.
Puri, Shruti; McMahon, Peter; Yamamoto, Yoshihisa
2014-03-01
The quantum non-demolition (QND) measurement of a single electron spin is of great importance in measurement-based quantum computing schemes. The current single-shot readout demonstrations exhibit substantial spin-flip backaction. We propose a QND readout scheme for quantum dot (QD) electron spins in Faraday geometry, which differs from previous proposals and implementations in that it relies on a novel physical mechanism: the spin-dependent Coulomb exchange interaction between a QD spin and optically-excited quantum well (QW) microcavity exciton-polaritons. The Coulomb exchange interaction causes a spin-dependent shift in the resonance energy of the polarized polaritons, thus causing the phase and intensity response of left circularly polarized light to be different to that of the right circularly polarized light. As a result the QD electron's spin can be inferred from the response to a linearly polarized probe. We show that by a careful design of the system, any spin-flip backaction can be eliminated and a QND measurement of the QD electron spin can be performed within a few 10's of nanoseconds with fidelity 99:95%. This improves upon current optical QD spin readout techniques across multiple metrics, including fidelity, speed and scalability. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan.
A scheme of quantum state discrimination over specified states via weak-value measurement
Chen, Xi; Dai, Hong-Yi; Liu, Bo-Yang; Zhang, Ming
2018-04-01
The commonly adopted projective measurements are invalid in the specified task of quantum state discrimination when the discriminated states are superposition of planar-position basis states whose complex-number probability amplitudes have the same magnitude but different phases. Therefore we propose a corresponding scheme via weak-value measurement and examine the feasibility of this scheme. Furthermore, the role of the weak-value measurement in quantum state discrimination is analyzed and compared with one in quantum state tomography in this Letter.
The role of scalar product and Wigner distribution in optical and quantum mechanical measurements
International Nuclear Information System (INIS)
Wodkiewicz, K.
1984-01-01
In this paper we present a unified approach to the phase-space description of optical and quantum measurements. We find that from the operational point of view the notion of a time dependent spectrum of light and a joint measurement of position and momentum in quantum mechanics can be formulated in one common approach in which the scalar product, the Wigner function and the phase-space proximity are closely related to a realistic measuring process
Quantum signatures of chaos or quantum chaos?
Energy Technology Data Exchange (ETDEWEB)
Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)
2016-11-15
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
Quantum signatures of chaos or quantum chaos?
International Nuclear Information System (INIS)
Bunakov, V. E.
2016-01-01
A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.
New CNB measures to stimulate credit growth: problems and solutions
Vidakovic, Neven; Zbašnik, Dušan
2014-01-01
The paper analyses the new measure implemented by Croatian national bank (CNB). The measure is a decrease in the reserve requirement, but the actual release of funds is contingent on increase in lending to firms. This new measure is significant because for the first time in Croatia there is a measure whose purpose is to affect specifically credit policy of the banks. Although this new measure has good intentions it does not solve the problem of why highly liquid banking system in Croatia is n...
Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback
Ruskov, Rusko; Schwab, Keith; Korotkov, Alexander N.
2005-06-01
We analyze squeezing of the nanoresonator state produced by periodic measurement of position by a quantum point contact or a single-electron transistor. The mechanism of squeezing is the stroboscopic quantum nondemolition measurement generalized to the case of continuous measurement by a weakly coupled detector. The magnitude of squeezing is calculated for the harmonic and stroboscopic modulations of measurement, taking into account detector efficiency and nanoresonator quality factor. We also analyze the operation of the quantum feedback, which prevents fluctuations of the wave packet center due to measurement back-action. Verification of the squeezed state can be performed in almost the same way as its preparation; a similar procedure can also be used for the force detection with sensitivity beyond the standard quantum limit.