Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction.
Quantum Operations as Quantum States
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2004-01-01
In this article we formalize the correspondence between quantum states and quantum operations, and harness its consequences. This correspondence was already implicit in Choi's proof of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived as simple corollaries of those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we search for more results to arise from the correspondence. Thus we propose a factorizability condition and an extremal trace-preservedness condition for quantum operations, give two novel Schmidt-type decompositions of bipartite pure states and two interesting composition laws for which the set of quantum operations and quantum states remain stable. The latter enables us to define a group structure upon the set of totally entangled state...
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations.The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations.It includes remote state preparation by using any pure entangled states,nonlocal operation implementation using entangled states,entanglement capacity of two-qubit gates and two-qubit gates construction.
Cohering power of quantum operations
Energy Technology Data Exchange (ETDEWEB)
Bu, Kaifeng, E-mail: bkf@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China); Kumar, Asutosh, E-mail: asukumar@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India); Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094 (India); Zhang, Lin, E-mail: linyz@zju.edu.cn [Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China); Wu, Junde, E-mail: wjd@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)
2017-05-18
Highlights: • Quantum coherence. • Cohering power: production of quantum coherence by quantum operations. • Study of cohering power and generalized cohering power, and their comparison for differentmeasures of quantum coherence. • Operational interpretation of cohering power. • Bound on cohering power of a generic quantum operation. - Abstract: Quantum coherence and entanglement, which play a crucial role in quantum information processing tasks, are usually fragile under decoherence. Therefore, the production of quantum coherence by quantum operations is important to preserve quantum correlations including entanglement. In this paper, we study cohering power–the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.
Operational interpretations of quantum discord
Cavalcanti, D; Boixo, S; Modi, K; Piani, M; Winter, A
2010-01-01
Quantum discord is a quantifier of non-classical correlations that goes beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms on consumption of entanglement in an extended quantum state merging protocol. We go on to show that the asymmetry of quantum discord is related to the performance imbalance in quantum state merging and dense coding.
Quantum quadratic operators and processes
Mukhamedov, Farrukh
2015-01-01
Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.
Energy Technology Data Exchange (ETDEWEB)
Bruzda, Wojciech [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: wojtek@gorce.if.uj.edu.pl; Cappellini, Valerio [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Zyczkowski, Karol [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warszawa (Poland)
2009-01-12
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator {phi} associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of {phi} and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.
Remote implementation of quantum operations
Energy Technology Data Exchange (ETDEWEB)
Huelga, Susana F [Quantum Physics Group, STRI, Department of Physics, Astrophysics and Mathematics, University of Hertfordshire, Hatfield, Herts AL10 9AB (United Kingdom); Plenio, Martin B [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom); Xiang Guoyong [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China); Li Jian [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China); Guo Guangcan [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China)
2005-10-01
Shared entanglement allows, under certain conditions, the remote implementation of quantum operations. We revise and extend recent theoretical results on the remote control of quantum systems as well as experimental results on the remote manipulation of photonic qubits via linear optical elements.
Remote Implementation of Quantum Operations
Huelga, S F; Xiang, G Y; Guo, J L G C; Huelga, Susana F.; Plenio, Martin B.; Xiang, Guo-Yong; Guo, Jian Li}and Guang-Can
2005-01-01
Shared entanglement allows, under certain conditions, the remote implementation of quantum operations. We revise and extend recent theoretical results on the remote control of quantum systems as well as experimental results on the remote manipulation of photonic qubits via linear optical elements.
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
Hierarchies of incoherent quantum operations
Streltsov, Alexander; Bera, Manabendra Nath; Lewenstein, Maciej
2015-01-01
The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in...
Unknowability of Quantum State forbids perfectly quantum operations
Institute of Scientific and Technical Information of China (English)
CAIQing-yu; LIBai-wen
2004-01-01
We analyze the oonnection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.
Unknowability of Quantum State forbids perfectly quantum operations
Institute of Scientific and Technical Information of China (English)
CAI Qing-yu; LI Bai-wen
2004-01-01
We analyze the connection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-07-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
Entanglement Mapping VS. Quantum Conditional Probability Operator
Chruściński, Dariusz; Kossakowski, Andrzej; Matsuoka, Takashi; Ohya, Masanori
2011-01-01
The relation between two methods which construct the density operator on composite system is shown. One of them is called an entanglement mapping and another one is called a quantum conditional probability operator. On the base of this relation we discuss the quantum correlation by means of some types of quantum entropy.
General description of discriminating quantum operations
Institute of Scientific and Technical Information of China (English)
Zhang Ke-Jia; Zhu Ping; Gao Fei; Guo Fen-Zhuo; Qin Su-Juan; Wen Qiao-Yan
2011-01-01
The discrimination of quantum operations plays a key role in quantum information and computation.Unlike discriminating quantum states,it has some special properties which can be carried out in practice.In this paper,we provide a general description of discriminating quantum operations.Concretely speaking,we describe the distinguishability between quantum operations using a measure called operator fidelity.It is shown that,employing the theory of operator fidelity,we can not only verify some previous results to discriminate unitary operations,but also exhibit a more general discrimination condition.We further apply our results to analysing the security of some quantum cryptographic protocols and discuss the realization of our method using well-developed quantum algorithms.
Atomic quantum transistor based on swapping operation
Moiseev, Sergey A; Moiseev, Eugene S
2011-01-01
We propose an atomic quantum transistor based on exchange by virtual photons between two atomic systems through the control gate-atom. The quantum transistor is realized in two QED cavities coupled in nano-optical scheme. We have found novel effect in quantum dynamics of coupled three-node atomic system which provides control-SWAP(\\theta) processes in quantum transistor operation. New possibilities of quantum entanglement in an example of bright and dark qubit states have been demonstrated for quantum transport in the atomic chain. Potentialities of the proposed nano-optical design for quantum computing and fundamental issues of multi-atomic physics are also discussed.
A quantum genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio
2013-11-01
In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Difference equations of quantum current operators and quantum parafermion construction
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\\hat x^\\pm(zq^{\\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\\hat {\\frak sl}(2))$.
Remote Operation on Quantum State Among Multiparty
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a scheme is proposed for performing remote operation on quantum state among multiparty.We use three-particle GHZ state as quantum channels to prepare a state operator, which describes quantum correlation between states and operations. Based on the special characteristic of the state operator, observers can perform unitary operation on a system that is away from observers. Our studies show this process is deterministic. We further consider remote operation among N spatially distributed observers, and the results show the successful realization of remote operation needs collective participation of N parties, that is, there exists strong correlation among multiparty. In addition, we investigate the case in which observers share a three-particle W state as quantum channels to perform remote operation and studies find this process is probabilistic.
The operational meaning of quantum conditional information
Devetak, I; Devetak, Igor; Yard, Jon
2006-01-01
With a statistical view towards information and noise, information theory derives ultimate limitations on information processing tasks. These limits are generally expressed in terms of entropic measures of information and correlations. Here we answer the quantum information-theoretic question: ``How correlated are two quantum systems from the perspective of a third?" by solving the following `quantum state redistribution' problem. Given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, what is the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob? The communication cost gives the first operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
The quantum phase operator a review
Barnett, Stephen M
2013-01-01
Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory. Bringing together vital works that have been publ
Simulation of n-qubit quantum systems. III. Quantum operations
Radtke, T.; Fritzsche, S.
2007-05-01
During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems
Operator representations on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Bauer, C.; Wachter, H. [Sektion Physik, Ludwig-Maximilians-Universitaet, Theresienstr. 37, 80333, Muenchen (Germany)
2003-11-01
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jackson's q-derivative to three and four dimensions. (orig.)
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.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Quantum remote control Teleportation of unitary operations
Huelga, S F; Chefles, A; Plenio, M B
2001-01-01
We consider the implementation of an unknown arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate the protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
On spectral theory of quantum vertex operators
Etingof, P
1994-01-01
In this note we prove the Davies-Foda-Jimbo-Miwa-Nakayashiki conjecture on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra U_q(\\hat sl_2), as n goes to infinity. For this purpose we define and study the leading eigenvalue and eigenvector of the product of two components of the quantum vertex operator. This eigenvector and the corresponding eigenvalue were recently computed by M.Jimbo. The results of his computation are given in Section 4.
A class of symmetric controlled quantum operations
Vaccaro, J A; Huelga, S F; Vaccaro, John A.
2001-01-01
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric.
A class of symmetric controlled quantum operations
Energy Technology Data Exchange (ETDEWEB)
Vaccaro, John A.; Steuernagel, O.; Huelga, S.F. [Division of Physics and Astronomy, Department of Physical Sciences, University of Hertfordshire, Hatfield (United Kingdom)
2001-09-07
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric. (author)
Unknown Quantum States and Operations, a Bayesian View
Fuchs, C; Fuchs, Christopher A.; Schack, Ruediger
2004-01-01
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states ...
Raising and lowering operators for quantum billiards
Indian Academy of Sciences (India)
AYUSH KUMAR MANDWAL; SUDHIR R JAIN
2017-09-01
For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m$, $n$, the index which represents a class is $c = m$ mod $kn$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by the application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.
New length operator for loop quantum gravity
Ma, Yongge; Yang, Jinsong
2010-01-01
An alternative expression for the length operator in loop quantum gravity is presented. The operator is background-independent, symmetric, positive semi-definite, and well-defined on the kinematical Hilbert space. The expression for the regularized length operator can moreover be understood both from a simple geometrical perspective as the average of a formula relating the length to area, volume and flux operators, and also consistently as the result of direct substitution of the densitized triad operator with the functional derivative operator into the regularized expression of the length. Both these derivations are discussed, and the origin of an undetermined overall factor in each case is also elucidated.
Hilbert Space Operators in Quantum Physics
Blank, Jiří; Havlíček, Miloslav
2008-01-01
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...
Entropic characterization of quantum operations
Roga, Wojciech; Zyczkowski, Karol
2011-01-01
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel {\\Phi}1 acting on a finite dimensional system there exists a class of channels {\\Phi}2 sufficiently close to a unitary map such that additivity of minimal output entropy for {\\Psi}1 x {\\Psi}2 holds.
Operational meaning of quantum measures of recovery
Cooney, Tom; Hirche, Christoph; Morgan, Ciara; Olson, Jonathan P.; Seshadreesan, Kaushik P.; Watrous, John; Wilde, Mark M.
2016-08-01
Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems A B C , by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.
Effective operator formalism for open quantum systems
DEFF Research Database (Denmark)
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...
Control through operators for quantum chemistry
Laurent, Philippe; Salomon, Julien; Turinici, Gabriel
2012-01-01
We consider the problem of operator identification in quantum control. The free Hamiltonian and the dipole moment are searched such that a given target state is reached at a given time. A local existence result is obtained. As a by-product, our works reveals necessary conditions on the laser field to make the identification feasible. In the last part of this work, some algorithms are proposed to compute effectively these operators.
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
Quantum operations: technical or fundamental challenge?
Mielnik, Bogdan
2013-09-01
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as ‘operation factories’ transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, while some others may verify the existence of fundamental precision limits of the position measurements or the reality of ‘non-commutative geometries’.
Check-Operators and Quantum Spectral Curves
Mironov, Andrei; Morozov, Alexei
2017-06-01
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model representatives.
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
We construct a commutative current operator $\\bar x^+(z)$ inside $U_q(\\hat{\\frak sl}(2))$. With this operator and the condition of quantum integrability on the quantum current of $U_q(\\hat{\\frak sl}(2))$, we derive the quantization of the semi-infinite construction of integrable modules of The quantization of the functional models for $\\hat{\\frak sl}(2)$ are also given.
Effective operator formalism for open quantum systems
DEFF Research Database (Denmark)
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...... involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method...
Pseudo-random unitary operators for quantum information processing.
Emerson, Joseph; Weinstein, Yaakov S; Saraceno, Marcos; Lloyd, Seth; Cory, David G
2003-12-19
In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of random unitary operators most relevant to quantum information tasks. This method requires exponentially fewer resources, and hence enables the practical application of random unitary operators in quantum communication and information processing protocols. Using a nuclear magnetic resonance quantum processor, we were able to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements.
The non-local content of quantum operations
Collins, D; Popescu, S; Collins, Daniel; Linden, Noah; Popescu, Sandu
2000-01-01
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyse classical communication from a quantum action.
Operational General Relativity: Possibilistic, Probabilistic, and Quantum
Hardy, Lucien
2016-01-01
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents' actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabiliti...
Wave operator theory of quantum dynamics
Durand, Philippe; Paidarová, Ivana
1998-09-01
An energy-dependent wave operator theory of quantum dynamics is derived for time-independent and time-dependent Hamiltonians. Relationships between Green's functions, wave operators, and effective Hamiltonians are investigated. Analytical properties of these quantities are especially relevant for studying resonances. A derivation of the relationship between the Green's functions and the (t,t') method of Peskin and Moiseyev [J. Chem. Phys. 99, 4590 (1993)] is presented. The observable quantities can be derived from the wave operators determined with the use of efficient iterative procedures. As in the theory of Bloch operators for bound states, the theory is based on a partition of the full Hilbert space into three subspaces: the model space, an intermediate space, and the outer space. On the basis of this partition an alternative definition of active spaces currently considered in large scale calculations is suggested. A numerical illustration is presented for several model systems and for the Stark effect in the hydrogen atom.
State-independent purity and fidelity of quantum operations
Kong, Fan-Zhen; Zong, Xiao-Lan; Yang, Ming; Cao, Zhuo-Liang
2016-04-01
The purity and fidelity of quantum operations are of great importance in characterizing the quality of quantum operations. The currently available definitions of the purity and fidelity of quantum operations are based on the average over all possible input pure quantum states, i.e. they are state-dependent (SD). In this paper, without resorting to quantum states, we define the state-independent (SI) purity and fidelity of a general quantum operation (evolution) in virtue of a new density matrix formalism for quantum operations, which is extended from the quantum state level to quantum operation level. The SI purity and fidelity gain more intrinsic physical properties of quantum operations than state-dependent ones, such as the purity of a one-qubit amplitude damping channel (with damping rate 1) is 1/2, which is in line with the fact that the channel is still a nonunitary operation described by two Kraus operators rather than a unitary one. But the state-dependent Haar average purity is 1 in this case. So the SI purity and fidelity proposed here can help the experimentalists to exactly quantify the implementation quality of an operation. As a byproduct, a new measure of the operator entanglement is proposed for a quantum evolution (unitary or nonunitary) in terms of the linear entropy of its density matrix on the orthonormal operator bases (OOBs) in Hilbert-Schmidt space.
Matrix Operator Approach to Quantum Evolution Operator and Geometric Phase
Kim, Sang Pyo; Soh, Kwang Sup
2012-01-01
The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix operator approach formulated in the product integral (PI) provides not only a method to find wave function efficiently in the MEH approach but also higher order corrections to the effective action systematically in the MEL approach, a la the Magnus expansion and the Kubo's cumulant expansion. A coupled quantum system of a light particle of harmonic oscillator is worked out, and as a by-product a new kind of gauge potential (Berry's connection) is found even for nondegenerate case (real eigenfunctions). Moreover, in the PI formulation the holonomy of the induced gauge potential is related to the Schlesinger's exact formula for the gauge field tensor. A superadiabatic expansion is also constructed and a generalized Dykhne formula, depending on the contour integrals of homotopy class of ...
Three paths toward the quantum angle operator
Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon
2016-12-01
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin-Klauder approaches. One method pertains to Weyl-Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of "weight" functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.
Linear Transformation Theory of Quantum Field Operators and Its Applications
Institute of Scientific and Technical Information of China (English)
MA Lei
2003-01-01
We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.
Control of Exciton Dynamics in Nanodots for Quantum Operations
Chen, Pochung; Piermarocchi, C.; Sham, L. J.
2001-08-01
We present a theory to further a new perspective of proactive control of exciton dynamics in the quantum limit. Circularly polarized optical pulses in a semiconductor nanodot are used to control the dynamics of two interacting excitons of opposite polarizations. Shaping of femtosecond laser pulses keeps the quantum operation within the decoherence time. Computation of the fidelity of the operations and application to the complete solution of a minimal quantum computing algorithm demonstrate in theory the feasibility of quantum control.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
Institute of Scientific and Technical Information of China (English)
FANHong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two panicles' relative coordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantum point-mass pendulum. The Hamiltonian displays the correct Schroedlnger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation are derived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Zeros and poles of quantum current operators and the condition of quantum integrability
Ding, J; Ding, Jintai; Miwa, Tetsuji
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current of $U_q\\left(\\hat{\\frak sl}(2)\\right)$, which is a deformation of the corresponding condition for $\\hat{\\frak sl}(2)$.
Quantum canonical ensemble: A projection operator approach
Magnus, Wim; Lemmens, Lucien; Brosens, Fons
2017-09-01
Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.
Minimum construction of two-qubit quantum operations
Zhang, J; Sastry, S; Whaley, K B; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. We also demonstrate that for the highly scalable Josephson junction charge qubits, the B gate is also more easily and quickly generated than the CNOT gate for physically feasible parameters.
Hybrid protocol of remote implementations of quantum operations
Zhao, Ning Bo; Wang, An Min
2007-12-01
We propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum-state teleportation (BQST) [Huelga , Phys. Rev. A 63, 042303 (2001)] and the Wang protocol [Wang, Phys. Rev. A 74, 032317 (2006)]. The protocol is available for remote implementations of quantum operations in the restricted sets specified in the paper. We also give a proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to the BQST and Wang protocols.
Implementation of nonlocal quantum swap operation on two entangled pairs
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 陈立冰; 郭光灿
2002-01-01
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resourcesof the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
A Note on Dirac Operators on the Quantum Punctured Disk
Directory of Open Access Journals (Sweden)
Slawomir Klimek
2010-07-01
Full Text Available We study quantum analogs of the Dirac type operator −2z∂/∂z on the punctured disk, subject to the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the quantum operator and show that it is bounded outside of the zero mode.
Non-selfadjoint operators in quantum physics mathematical aspects
Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon; Znojil, Miloslav
2015-01-01
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses recent emergence of the unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis, with potentially significant physical consequences. In addition to prompting a discussion of the role of mathematical methods in the contemporary development of quantum physics, the book features: * Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area *...
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Protected quantum computing: interleaving gate operations with dynamical decoupling sequences.
Zhang, Jingfu; Souza, Alexandre M; Brandao, Frederico Dias; Suter, Dieter
2014-02-07
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.
Remote implementations of partially known quantum operations of multiqubits
Wang, A M
2005-01-01
Based on our simplified HPV's scheme for one qubit, we investigate the remote implementations of the partially known quantum operations (within some restricted sets that satisfy the given conditions). After giving out the obvious forms of eight interesting restricted sets of quantum operations of two qubits, we propose the protocol of the remote implementations of them using a universal recovered operation performed by the receiver. Furthermore, we show the extension of our protocol to the case of multiqubits.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two particles'relativecoordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantumpoint-mass pendulum. The Hamiltonian displays the correct Schrodinger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation arederived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Lectures on algebraic quantum field theory and operator algebras
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Berlin Univ. (Germany). Institut fuer Theoretische Physik. E-mail: schroer@cbpf.br
2001-04-01
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)
Efficient quantum circuits for dense circulant and circulant like operators
Zhou, S. S.; Wang, J. B.
2017-05-01
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed.
Qubit-Programmable Operations on Quantum Light Fields.
Barbieri, Marco; Spagnolo, Nicolò; Ferreyrol, Franck; Blandino, Rémi; Smith, Brian J; Tualle-Brouri, Rosa
2015-10-15
Engineering quantum operations is a crucial capability needed for developing quantum technologies and designing new fundamental physics tests. Here we propose a scheme for realising a controlled operation acting on a travelling continuous-variable quantum field, whose functioning is determined by a discrete input qubit. This opens a new avenue for exploiting advantages of both information encoding approaches. Furthermore, this approach allows for the program itself to be in a superposition of operations, and as a result it can be used within a quantum processor, where coherences must be maintained. Our study can find interest not only in general quantum state engineering and information protocols, but also details an interface between different physical platforms. Potential applications can be found in linking optical qubits to optical systems for which coupling is best described in terms of their continuous variables, such as optomechanical devices.
Zhang, KeJia; Zhang, Long; Song, TingTing; Yang, YingHui
2016-06-01
In this paper, we propose certain different design ideas on a novel topic in quantum cryptography — quantum operation sharing (QOS). Following these unique ideas, three QOS schemes, the "HIEC" (The scheme whose messages are hidden in the entanglement correlation), "HIAO" (The scheme whose messages are hidden with the assistant operations) and "HIMB" (The scheme whose messages are hidden in the selected measurement basis), have been presented to share the single-qubit operations determinately on target states in a remote node. These schemes only require Bell states as quantum resources. Therefore, they can be directly applied in quantum networks, since Bell states are considered the basic quantum channels in quantum networks. Furthermore, after analyse on the security and resource consumptions, the task of QOS can be achieved securely and effectively in these schemes.
Security of Quantum Repeater Network Operation
2016-10-03
enumerating differences from classical networks. Quantum networks, of course, depend upon successful creation of high-fidelity entanglement at the link...is equivalent to the classical Internet silently corrupting data somewhere along a network path without the benefit of hop-by-hop error detection...for nodes intended to form a future Quantum Internet be required to support two classes of physically distinct qubits inside the DISTRIBUTION A
The Dirac operator and gamma matrices for quantum Minkowski spaces
1997-01-01
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
New scalar constraint operator for loop quantum gravity
Assanioussi, Mehdi; Mäkinen, Ilkka
2015-01-01
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of...
Junctions of surface operators and categorification of quantum groups
Chun, Sungbong; Roggenkamp, Daniel
2015-01-01
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-01-01
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2016-05-01
We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.
Universal programmable quantum circuit schemes to emulate an operator.
Daskin, Anmer; Grama, Ananth; Kollias, Giorgos; Kais, Sabre
2012-12-21
Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U = e(-iHt) for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.
Why Do the Quantum Observables Form a Jordan Operator Algebra?
Niestegge, Gerd
2010-01-01
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in a recent paper, it is shown in this paper that such a multiplication operation can be derived from certain properties of the conditional probabilities and the observables, i.e., from postulates with a clear statistical interpretation. The well-known close relation between Jordan operator algebras and C*-algebras then provides the connection to the quantum-mechanical Hilbert space formalism, thus resulting in a novel axiomatic approach to general quantum mechanics that includes the types II and III von Neumann algebras.
Operators versus functions: from quantum dynamical semigroups to tomographic semigroups
Aniello, Paolo
2013-11-01
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disguise', namely, by a semigroup of operators acting on tomograms rather than on density operators. We focus on a special class of quantum dynamical semigroups, the twirling semigroups, that have interesting applications, e.g., in quantum information science. The 'disguised counterparts' of the twirling semigroups, i.e., the corresponding semigroups acting on tomograms, form a class of semigroups of operators that we call tomographic semigroups. We show that the twirling semigroups and the tomographic semigroups can be encompassed in a unique theoretical framework, a class of semigroups of operators including also the probability semigroups of classical probability theory, so achieving a deeper insight into both the mathematical and the physical aspects of the problem.
Matrix Product Operator Simulations of Quantum Algorithms
2015-02-01
Communications, pages 174–188. Springer, 1999. Bibliography 145 [21] Michelangelo Grigni, Leonard Schulman, Monica Vazirani, and Umesh Vazirani...2007. [27] Andrew M Childs, Leonard J Schulman, and Umesh V Vazirani. Quan- tum algorithms for hidden nonlinear structures. In Foundations of...and quantum in- formation. Cambridge University Press, Cambridge, 2000. [86] Charles H Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani
Security of Quantum Repeater Network Operation
2016-10-03
15. SUBJECT TERMS Quantum Architecture 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18. NUMBER OF PAGES 5 19a. NAME OF...22 Rodney Van Meter Associate Professor, Faculty of Environment and Information Studies Keio University, Japan +81-90-8012-3643 rdv@sfc.keio.ac.jp
The thermodynamic cost of quantum operations
Bedingham, D. J.; Maroney, O. J. E.
2016-11-01
The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower bound is set by the Landauer limit, at which computation becomes thermodynamically reversible. For classical computation there is no physical principle which prevents this limit being reached, and approaches to it are already being experimentally tested. In this paper we show that for quantum computation with a set of signal states satisfying given conditions, there is an unavoidable excess heat generation that renders it inherently thermodynamically irreversible. The Landauer limit cannot, in general, be reached by quantum computers. We show the existence of a lower bound to the heat generated by quantum computing that exceeds that given by the Landauer limit, give the special conditions where this excess cost may be avoided, and provide a protocol for achieving the limiting heat cost when these conditions are met. We also show how classical computing falls within the special conditions.
A method of extracting operating parameters of a quantum circuit
Sete, Eyob A.; Block, Maxwell; Scheer, Michael; Zanoci, Cris; Vahidpour, Mehrnoosh; Thompson, Dane; Rigetti, Chad
Rigorous simulation-driven design methods are an essential component of traditional integrated circuit design. We adapt these techniques to the design and development of superconducting quantum integrated circuits by combining classical finite element analysis in the microwave domain with Brune circuit synthesis by Solgun [PhD thesis 2014] and BKD Hamiltonian analysis by Burkard et al. [Phys. Rev. B 69, 064503 (2004)]. Using the Hamiltonian of the quantum circuit, constructed using the synthesized equivalent linear circuit and the nonlinear Josephson junctions' contributions, we extract operating parameters of the quantum circuit such as resonance coupling strength, dispersive shift, qubit anharmonicitiy, and decoherence rates for single-and multi-port quantum circuits. This approach has been experimentally validated and allows the closed-loop iterative simulation-driven development of quantum information processing devices.
On Quantum Field Theories in Operator and Functional Integral Formalisms
Teleki, A; Noga, Milan; Teleki, Aba
2006-01-01
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional integral in quantum field theory cannot be regarded as a Newton-Lebesgue integral but rather as a formal object to which one associates distinct numerical values for different processes of its integration. By choosing an appropriate method for the integration of a given functional integral, one can select a single representation out of infinitely many inequivalent representations for an operator whose trace is expressed by the corresponding functional integral. These properties are demonstrated with two exactly solvable examples.
GENERALIZED OPERATORS AND P(φ)2 QUANTUM FIELDS
Institute of Scientific and Technical Information of China (English)
黄志远; 让光林
2004-01-01
In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.
Operating single quantum emitters with a compact Stirling cryocooler
Energy Technology Data Exchange (ETDEWEB)
Schlehahn, A.; Krüger, L.; Gschrey, M.; Schulze, J.-H.; Rodt, S.; Strittmatter, A.; Heindel, T., E-mail: tobias.heindel@tu-berlin.de; Reitzenstein, S. [Institute of Solid State Physics, Technische Universität Berlin, 10623 Berlin (Germany)
2015-01-15
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g{sup (2)}(0) < 0.04 from this Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g{sup (2)}(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Operating single quantum emitters with a compact Stirling cryocooler.
Schlehahn, A; Krüger, L; Gschrey, M; Schulze, J-H; Rodt, S; Strittmatter, A; Heindel, T; Reitzenstein, S
2015-01-01
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g((2))(0) Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g((2))(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Operating single quantum emitters with a compact Stirling cryocooler
Schlehahn, A.; Krüger, L.; Gschrey, M.; Schulze, J.-H.; Rodt, S.; Strittmatter, A.; Heindel, T.; Reitzenstein, S.
2015-01-01
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g(2)(0) < 0.04 from this Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g(2)(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Quantum hidden Markov models based on transition operation matrices
Cholewa, Michał; Gawron, Piotr; Głomb, Przemysław; Kurzyk, Dariusz
2017-04-01
In this work, we extend the idea of quantum Markov chains (Gudder in J Math Phys 49(7):072105 [3]) in order to propose quantum hidden Markov models (QHMMs). For that, we use the notions of transition operation matrices and vector states, which are an extension of classical stochastic matrices and probability distributions. Our main result is the Mealy QHMM formulation and proofs of algorithms needed for application of this model: Forward for general case and Vitterbi for a restricted class of QHMMs. We show the relations of the proposed model to other quantum HMM propositions and present an example of application.
Tailored jump operators for purely dissipative quantum magnetism
Weimer, Hendrik
2017-01-01
I propose an architecture for the realization of dissipative quantum many-body spin models. The dissipative processes are mediated by interactions with auxiliary particles and lead to a widely tunable class of correlated quantum jump operators. These findings enable the investigation of purely dissipative spin models, where coherent dynamics is entirely absent. I provide a detailed review of a recently introduced variational method to analyze such dissipative quantum many-body systems, and I discuss a specific example in terms of a purely dissipative Heisenberg model, for which I find an additional disordered phase that is not present in the corresponding ground state phase diagram.
Tailored jump operators for purely dissipative quantum magnetism
Weimer, Hendrik
2016-01-01
I propose an archtitecture for the realization of dissipative quantum many-body spin models. The dissipative processes are mediated by interactions with auxiliary particles and lead to a widely tunable class of correlated quantum jump operators. These findings enable the investigation of purely dissipative spin models, where coherent dynamics is entirely absent. I provide a detailed review of a recently introduced variational method to analyze such dissipative quantum many-body systems, and I discuss a specific example in terms of a purely dissipative Heisenberg model, for which I find an additional disordered phase that is not present in the corresponding ground state phase diagram.
Zhou, Nanrun; Hu, Yiqun; Gong, Lihua; Li, Guangyong
2017-06-01
A new quantum image encryption scheme is suggested by using the iterative generalized Arnold transforms and the quantum image cycle shift operations. The times of the quantum image cycle shift operations are controlled by a hyper-chaotic sequence generated by a new 4D hyper-chaotic system. The image pixels are scrambled by the iterative generalized Arnold transform, and the values of the pixels are altered by the quantum image cycle shift operations. The four initial conditions of the new 4D hyper-chaotic system are exploited to control the two parameters, the iterative rounds of the generalized Arnold transform and the times of the quantum image cycle shift operations, respectively. Thus, the main keys of the proposed quantum image encryption scheme are the four initial conditions of the new 4D hyper-chaotic system and the key space is relatively large enough. Simulation results and theoretical analyses demonstrate that the proposed quantum image encryption scheme outperforms its classical counterparts apparently.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Micho Đurđevich; Stephen Bruce Sontz
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators amo...
Quantum Operator Design for Lattice Baryon Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Lichtl, Adam [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2006-09-07
A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.
Foundations of quantum theory from classical concepts to operator algebras
Landsman, Klaas
2017-01-01
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.
Characterizing quantum phase transitions by single qubit operations
Giampaolo, S M; De Siena, S
2006-01-01
We introduce observable quantities, borrowing from concepts of quantum information theory, for the characterization of quantum phase transitions in spin systems. These observables are uniquely defined in terms of single spin unitary operations. We define the energy gap between the ground state and the state produced by the action of a single-qubit local gate. We show that this static quantity involves only single-site expectations and two-point correlation functions on the ground state. We then discuss a dynamical local observable defined as the acceleration of quantum state evolution after performing an instaneous single-qubit perturbation on the ground state. This quantity involves three-point correlations as well. We show that both the static and the dynamical observables detect and characterize completely quantum critical points in a class of spin systems.
Robust Solid State Quantum System Operating at 800 K
Kianinia, Mehran; Regan, Blake; Tran, Toan Trong; Ford, Michael J; Aharonovich, Igor; Toth, Milos
2016-01-01
Realization of Quantum information and communications technologies requires robust, stable solid state single photon sources. However, most existing sources cease to function above cryogenic or room temperature due to thermal ionization or strong phonon coupling which impede their emissive and quantum properties. Here we present an efficient single photon source based on a defect in a van der Waals crystal that is optically stable and operates at elevated temperatures of up to 800 K. The quantum nature of the source and the photon purity are maintained upon heating to 800 K and cooling back to room temperature. Our report of a robust high temperature solid state single photon source constitutes a significant step to-wards practical, integrated quantum technologies for real-world environments.
Random operators disorder effects on quantum spectra and dynamics
Aizenman, Michael
2015-01-01
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization-presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and rela...
Operators from mirror curves and the quantum dilogarithm
Kashaev, Rinat
2015-01-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local P2, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Operators from Mirror Curves and the Quantum Dilogarithm
Kashaev, Rinat; Mariño, Marcos
2016-09-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local {{P}^2}, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Influences of Gate Operation Errors in the Quantum Counting Algorithm
Institute of Scientific and Technical Information of China (English)
Qing Ai; Yan-Song Li; Gui-Lu Long
2006-01-01
In this article, the error analysis in the quantum counting algorithm is investigated. It has been found that the random error plays as important a role as the systematic error does in the phase inversion operations. Both systematic and random errors are important in the Hadamard transformation. This is quite different from the Grover algorithm and the Shor algorithm.
The Construction of Quantum Field Operators: Something of Interest
Dvoeglazov, Valeri V
2010-01-01
We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is paid to the chiral theories, and to the method of the Lorentz boosts.
Controlled remote implementation of partially unknown quantum operation
Institute of Scientific and Technical Information of China (English)
FAN QiuBo; LIU DongDong
2008-01-01
A protocol for controlled remote implementation of a partially unknown operation on an arbitrary quantum state is proposed. In this protocol, a task can be performed using a GHZ state shared among three distant parties: Alice, Bob and the controller Charlie. This protocol is also generalized to the multi-party control system based on sharing an N-qubit GHZ state.
Pseudo-Hermitian quantum mechanics with unbounded metric operators.
Mostafazadeh, Ali
2013-04-28
I extend the formulation of pseudo-Hermitian quantum mechanics to η(+)-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator η(+). In particular, I give the details of the construction of the physical Hilbert space, observables and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of η(+) and consequently √η(+).
Ihly, Rachelle
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic study of the absorption properties of PbS quantum dot films exposed to air, heat, and UV illumination as a function of quantum dot size has been described. A method to improve the air-stability of films with atomic layer deposition of alumina is demonstrated. Encapsulation of quantum dot films using a protective layer of alumina results in quantum dot solids that maintain tuned absorption for 1000 hours. This thesis focuses on the use of atomic force microscopy and electrical variants thereof to study the physical and electrical characteristics of quantum dot arrays. These types of studies have broad implications in understanding charge transport mechanisms and solar cell device operation, with a particular emphasis on quantum dot transistors and solar cells. Imaging the channel potential of a PbSe quantum dot thin-film in a transistor showed a uniform distribution of charge coinciding with the transistor current voltage characteristics. In a second study, solar cell device operation of ZnO/PbS heterojunction solar cells was investigated by scanning active cross-sections with Kelvin probe microscopy as a function of applied bias, illumination and device architecture. This technique directly provides operating potential and electric field profiles to characterize drift and diffusion currents occurring in the device. SKPM established a field-free region occurring in the quantum dot layer, indicative of diffusion-limited transport. These results provide the path to optimization of
A new theorem relating quantum tomogram to the Fresnel operator
Institute of Scientific and Technical Information of China (English)
Xie Chuan-Mei; Fan Hong-Yi
2011-01-01
According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinatemomentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator p is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.
Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots
Benguria, Rafael D.; Fournais, Søren; Stockmeyer, Edgardo; Van Den Bosch, Hanne
2017-06-01
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to |Ω|-1/2, where {Ω } \\subset R2 is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Durdevich, Micho; Sontz, Stephen Bruce
2013-05-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Directory of Open Access Journals (Sweden)
Micho Đurđevich
2013-05-01
Full Text Available A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
evich, Micho Đurđ
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutivity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Institute of Scientific and Technical Information of China (English)
FAN HongYi
2012-01-01
In quantum mechanics theory one of the basic operator orderings is Q - P and P - Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q - P ordering and P - Q ordering is introduced.The Q - P ordered and P - Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q - P or P - Q ordering much more convenient.
Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography.
Bonk, F A; deAzevedo, E R; Sarthour, R S; Bulnes, J D; Freitas, J C C; Guimarães, A P; Oliveira, I S; Bonagamba, T J
2005-08-01
This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.
Entanglement-assisted operator codeword stabilized quantum codes
Shin, Jeonghwan; Heo, Jun; Brun, Todd A.
2016-05-01
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct QECCs. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
The Quantum Field Theory of the Ensemble Operator
Porter, Richard N.
2009-03-01
Quantum field theory (QFT) provides a systematic investigative tool for ensembles of molecules. The grand-canonical ensemble operator (GCEO) for an ideal gas is presented in terms of the Fock creation and annihilation operators. The ideal GCEO can be shown to obey a simple equation which facilitates calculation of quantum-statistical properties of bosonic and fermionic molecules. Examples are linked-cluster QFT derivations of the grand-canonical partition function and the Poisson distribution for non-interacting molecules. The Boltzmann limit is achieved by omitting exchange diagrams. Summations of Feynman diagrams for long- and short-range interactions to infinite order lead to a useful model of the pair-correlation function and a new avenue for the study of dynamics near the critical point for gas-liquid phase transitions.
Fundamental Entangling Operators in Quantum Mechanics and Their Properties
Dao-Ming, Lu
2016-07-01
For the first time, we introduce so-called fundamental entangling operators e^{iQ1 P2} and e^{iP1 Q2 } for composing bipartite entangled states of continuum variables, where Q i and P i ( i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation ( q 1, q 2) → ( A q 1 + B q 2, C q 1 + D q 2), where A D- B C = 1, which means even the basic coordinate transformation ( Q 1, Q 2) → ( A Q 1 + B Q 2, C Q 1 + D Q 2) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.
Novotny, J; Jex, I
2006-01-01
The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.
The Diffeomorphism Constraint Operator in Loop Quantum Gravity
Laddha, Alok
2011-01-01
We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, evaluate its continuum limit on the Lewandowski- Marolf habitat and show that the action of the continuum operator provides an anomaly free representation of the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our analysis include: (i) finite triangulation approximants to the curvature, $F_{ab}^i$ of the Ashtekar- Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field (iii) continuum constraint operators which do {\\em not} have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterised field theory by the authors. Features (i) and (ii) provide ...
Quantum dimensions from local operator excitations in the Ising model
Caputa, Pawel
2016-01-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Renyi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as t...
Zhang, Jingfu; Laflamme, Raymond; Suter, Dieter
2012-09-07
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.
Bosonic Operator Realization of Hamiltonian for a Superconducting Quantum Interference Device
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2004-01-01
Based on the appropriate bosonic phase operator diagonalized in the entangled state representation we construct the Hamiltonian operator model for a superconducting quantum interference device. The current operator and voltage operator equations are derived.
Composition of quantum operations and products of random matrices
Roga, Wojciech; Zyczkowski, Karol
2011-01-01
Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing the composition of s random maps and demonstrate that their complex eigenvalues are asymptotically described by the law of Burda et al. obtained for a product of s independent random complex Ginibre matrices. Numerical data support the conjecture that the same results are applicable to characterize the distribution of eigenvalues of the s-th power of a random Ginibre matrix. Squared singular values of Psi are shown to be described by the Fuss-Catalan distribution of order s. Results obtained for products of random Ginibre matrices are also capable to describe the s-step evolution operator for a model deterministic dynamical system - a generalized quantum baker map subjected to strong interaction with an environm...
Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
Emerson, J
2003-01-01
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and generated on a quantum processor in a way that requires exponentially fewer resources than direct implementation of the uniformly random set. Efficient pseudo-random operators can overcome the exponential cost of random operators required for quantum communication tasks such as super-dense coding of quantum states and approximately secure quantum data-hiding, and enable efficient stochastic methods for noise estimation on prototype quantum processors. This paper summarizes some recently published work demonstrating a random circuit method for the implementation of pseudo-random unitary operators on a quantum processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further elaborates the theory and applications of pseudo-random states and operators.
Operational dynamic modeling transcending quantum and classical mechanics.
Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A
2012-11-09
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
Irreducible Tensor Operators and Multiple-Quantum NMR.
Hutchison, Wayne Douglas
The aim of the work detailed in this thesis, is to provide a concise, and illuminating, mathematical description of multiple quantum nuclear magnetic resonance (MQNMR) experiments, on essentially isolated (non-coupled) nuclei. The treatment used is based on irreducible tensor operators, which form an orthonormal basis set. Such operators can be used to detail the state of the nuclear ensemble (density matrix) during every stage, preparation, evolution and detection, of a MQNMR experiment. Moreover, such operators can be also used to provide a rigorous analysis of pulsed NMR experiments, on oriented nuclei at low temperatures, where the initial density matrix is far from trivial. The specific topics dealt with in this thesis are as follows. In the first place the properties of irreducible tensor operators are discussed in some detail. In particular, symmetric and anti-symmetric combinations of tensor operators are introduced, to reflect the Hermitian nature of the nuclear Hamiltonian and density matrix. Secondly, the creation of multipolar nuclear states using hard, non-selective rf pulses, is detailed for spin I = 1, 3/2, 2 and 5/2 nuclei, subject to an axially symmetric quadrupole interaction. Results are also given for general I. Thirdly, some experimental results, verifying the production of a triple quantum NMR state, for the I = 3/2 ^{23}Na nuclei in a single crystal of NaIO_4 are presented and discussed. Fourthly, the treatment of MQNMR experiments is extended to the low temperature regime where the initial density matrix includes Fano statistical tensors other than rank one. In particular, it is argued that MQNMR techniques could be used to enhance the anisotropy of gamma-ray emission from oriented nuclei at low temperatures. Fifthly, the effect of a more general quadrupole Hamiltonian (including an asymmetry term) on MQNMR experiments is considered for spins I = 1 and 3/2. In particular, it is shown that double quantum states evolve to give longitudinal NMR
Molecular machines operating on the nanoscale: from classical to quantum
Directory of Open Access Journals (Sweden)
Igor Goychuk
2016-03-01
Full Text Available The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.
Induced Ginibre ensemble of random matrices and quantum operations
Fischmann, J; Khoruzhenko, B A; Sommers, H -J; Zyczkowski, K
2011-01-01
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.
Quantum dimensions from local operator excitations in the Ising model
Caputa, Paweł; Rams, Marek M.
2017-02-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.
Semiclassical genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Nakahara, Mikio
2012-01-01
In order for finding a good individual for a given fitness function in the context of evolutionary computing, we introduce a novel semiclassical quantum genetic algorithm. It has both of quantum crossover and quantum mutation procedures unlike conventional quantum genetic algorithms. A complexity analysis shows a certain improvement over its classical counterpart.
Jorgensen, PET
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
Measures of coherence-generating power for quantum unital operations
Zanardi, Paolo; Styliaris, Georgios; Campos Venuti, Lorenzo
2017-05-01
Given an orthonormal basis B in a d -dimensional Hilbert space and a unital quantum operation E acting on it, one can define a nonlinear mapping that associates with E a d ×d real-valued matrix that we call the coherence matrix of E with respect to B . This is the Gram matrix of the coherent part of the basis projections of B under E . We show that one can use this coherence matrix to define vast families of measures of the coherence-generating power (CGP) of the operation. These measures have a natural geometrical interpretation as separation of E from the set of incoherent unital operations. The probabilistic approach to CGP discussed in P. Zanardi et al. [Phys. Rev. A 95, 052306 (2017)., 10.1103/PhysRevA.95.052306] can be reformulated and generalized, introducing, alongside the coherence matrix, another d ×d real-valued matrix, the simplex correlation matrix. This matrix describes the relevant statistical correlations in the input ensemble of incoherent states. Contracting these two matrices, one finds CGP measures associated with the process of preparing the given incoherent ensemble and processing it with the chosen unital operation. Finally, in the unitary case, we discuss how these concepts can be made compatible with an underlying tensor product structure by defining families of CGP measures that are additive.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Robustness of coherence: An operational and observable measure of quantum coherence
Napoli, Carmine; Cianciaruso, Marco; Piani, Marco; Johnston, Nathaniel; Adesso, Gerardo
2016-01-01
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase-discrimination task.
Entanglement Entropy of Local Operators in Quantum Lifshitz Theory
Zhou, Tianci
2016-01-01
We study the growth of entanglement entropy(EE) of local operator excitation in the quantum Lifshitz model which has dynamic exponent z = 2. Specifically, we act a local vertex operator on the groundstate at a distance $l$ to the entanglement cut and calculate the EE as a function of time for the state's subsequent time evolution. We find that the excess EE compared with the groundstate is a monotonically increasing function which is vanishingly small before the onset at $t \\sim l^2$ and eventually saturates to a constant proportional to the scaling dimension of the vertex operator. The quasi-particle picture can interpret the final saturation as the exhaustion of the quasi-particle pairs, while the diffusive nature of the time scale $t \\sim l^2$ replaces the common causality constraint in CFT calculation. To further understand this property, we compute the excess EE of a small disk probe far from the excitation point and find chromatography pattern in EE generated by quasi-particles of different propagation ...
Yao, Xing-Can; Fiurásek, Jaromír; Lu, He; Gao, Wei-Bo; Chen, Yu-Ao; Chen, Zeng-Bing; Pan, Jian-Wei
2010-09-17
We experimentally demonstrate an advanced linear-optical programmable quantum processor that combines two elementary single-qubit programmable quantum gates. We show that this scheme enables direct experimental probing of quantum commutation relations for Pauli operators acting on polarization states of single photons. Depending on a state of two-qubit program register, we can probe either commutation or anticommutation relations. Very good agreement between theory and experiment is observed, indicating high-quality performance of the implemented quantum processor.
2015-02-16
Microwave-driven coherent operation of a semiconductor quantum dot charge qubit Dohun Kim,1 D. R. Ward,1 C. B. Simmons,1 John King Gamble,2 Robin...Fig.4a. Coherent microwave ac-gating of a semiconductor quantum dot charge qubit offers fast ( >GHz) manip- ulation rates for all elementary rotation...2014). [12] Kim, D. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014). [13] Vion, D
Quantum walk through lattice with temporal, spatial, and fluctuating disordered operations
Chandrashekar, C M
2011-01-01
Quantum walks and its dynamic properties have provided a framework to various applications ranging from quantum computing to simulation of physical processes in nature. We present a discrete-time quantum walk model with the evolution operator for each step in the form of the Hamiltonian operator. The Hamiltonian form of the evolution operator is extended to define the discrete-time quantum walk using two-state particle on a two-dimensional lattice structure such as, triangular, kagome and honeycomb lattice. We also study the walk dynamics using temporal, spatially static, and fluctuating disordered unitary evolution operators and show that the localization is possible only with a spatially static disordered operations. This approach provides a general framework for using a two-state particle discrete-time quantum walk to simulate, control, and study the dynamics in form of ordered and disordered Hamiltonian operations in various one- and two-dimensional physical systems.
Lin, Jun-You; He, Jun-Gang; Gao, Yan-Chun; Li, Xue-Mei; Zhou, Ping
2017-04-01
We present a scheme for controlled remote implementation of an arbitrary single-qubit operation by using partially entangled states as the quantum channel. The sender can remote implement an arbitrary single-qubit operation on the remote receiver's quantum system via partially entangled states under the controller's control. The success probability for controlled remote implementation of quantum operation can achieve 1 if the sender and the controller perform proper projective measurements on their entangled particles. Moreover, we also discuss the scheme for remote sharing the partially unknown operations via partially entangled quantum channel. It is shown that the quantum entanglement cost and classical communication can be reduced if the implemented operation belongs to the restrict sets.
About the velocity operator for spinning particles in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Catania (Italy); Recami, Erasmo; Rodrigues Junior, Waldyr A. [Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada
1995-12-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs.
The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2003-01-01
We represent generalized density matrices of a $d$-complex dimensional quantum system as a subcone of a real pointed cone of revolution in $\\mathbb{R}^{d^2}$, or indeed a Minkowskian cone in $\\mathbb{E}^{1,d^2-1}$. Generalized pure states correspond to certain future-directed light-like vectors of $\\mathbb{E}^{1,d^2-1}$. This extension of the Generalized Bloch Sphere enables us to cater for non-trace-preserving quantum operations, and in particluar to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulae for the one qubit case and express the post-measurement states in terms of the initial state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance tradeoff in the case of two equiprobable pure states. Thus we recover Fuch's formula in an elegant manner.
On the maximum speed of operation of a quantum "black box"
Dugic, M
2001-01-01
We investigate the minimum time needed for (i.e. the maximum speed of) a quantum "black box" ("oracle") operation which employs "quantum parallelism" to be executed. We emphasize that the operation considered employs the quantum-measurement-like establishing of entanglement in the composite system "input register + output register" of a quantum computer's hardware, and we show that the speed of the operation can be increased by increasing the coupling (strength of interaction) in the composite system, as well as by some local operations (e.g., a proper state preparation) performed on the output register. It also proves that the operation employing a macroscopic (or at least a mesoscopic) system to mediate the registers' interaction should be much faster than the operation performed through direct registers' interaction. Finally, we show that adding energy to the composite system needs not to speed up the operation considered. Rather, e.g., in the case of mutually directly interacting registers, the requiremen...
Fraunhofer regime of operation for superconducting quantum interference filters
DEFF Research Database (Denmark)
Shadrin, A.V.; Constantinian, K.Y.; Ovsyannikov, G.A.;
2008-01-01
Series arrays of superconducting quantum interference devices (SQUIDs) with incommensurate loop areas, so-called superconducting quantum interference filters (SQIFs), are investigated in the kilohertz and the gigahertz frequency range. In SQIFs made of high-T-c bicrystal junctions the flux-to-vol...
Scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity
Nishimura, J; Tsuchiya, A; Jun Nishimura; Shinya Tamura; Asato Tsuchiya
1994-01-01
Using (2+$\\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$ minimal conformal matter. In the spectrum appear all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, while there are also many others which have no corresponding scaling dimensions in the matrix model.
An Operator-Based Exact Treatment of Open Quantum Systems
Nicolosi, S
2005-01-01
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. The theory of open quantum systems thus plays a major role in many applications of quantum physics since perfect isolation of quantum system is not possible and since a complete microscopic description or control of the environment degrees of freedom is not feasible or only partially so" [1]. Practical considerations therefore force one to seek for a simpler, effectively probabilistic description in terms of an open system. There is a close physical and mathematical connection between the evolution of an open system, the state changes induced by quantum measurements, and the classical notion of a stochastic process. The paper provides a bibliographic review of this interrelations, it shows the mathematical equivalence between markovian master equation and generaliz...
Rotta, Davide; Sebastiano, Fabio; Charbon, Edoardo; Prati, Enrico
2017-06-01
Even the quantum simulation of an apparently simple molecule such as Fe2S2 requires a considerable number of qubits of the order of 106, while more complex molecules such as alanine (C3H7NO2) require about a hundred times more. In order to assess such a multimillion scale of identical qubits and control lines, the silicon platform seems to be one of the most indicated routes as it naturally provides, together with qubit functionalities, the capability of nanometric, serial, and industrial-quality fabrication. The scaling trend of microelectronic devices predicting that computing power would double every 2 years, known as Moore's law, according to the new slope set after the 32-nm node of 2009, suggests that the technology roadmap will achieve the 3-nm manufacturability limit proposed by Kelly around 2020. Today, circuital quantum information processing architectures are predicted to take advantage from the scalability ensured by silicon technology. However, the maximum amount of quantum information per unit surface that can be stored in silicon-based qubits and the consequent space constraints on qubit operations have never been addressed so far. This represents one of the key parameters toward the implementation of quantum error correction for fault-tolerant quantum information processing and its dependence on the features of the technology node. The maximum quantum information per unit surface virtually storable and controllable in the compact exchange-only silicon double quantum dot qubit architecture is expressed as a function of the complementary metal-oxide-semiconductor technology node, so the size scale optimizing both physical qubit operation time and quantum error correction requirements is assessed by reviewing the physical and technological constraints. According to the requirements imposed by the quantum error correction method and the constraints given by the typical strength of the exchange coupling, we determine the workable operation frequency
2016-12-02
Networking with QUantum operationally-Secure Technology for Maritime Deployment (CONQUEST) Contract Period of Performance: 2 September 2016 – 1 September...potential of using advanced photonic integrated circuits to enable high- speed quantum-secure communications. Task 5: QKD network via un-trusted quantum...has a practical advantage in its imple- mentation since it can use conventional optical telecom components, and does not require cryostats to support
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
Directory of Open Access Journals (Sweden)
Masanao Ozawa
2017-01-01
Full Text Available In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance conditional. A fundamental problem is to show how the form of the conditional follows from an analysis of operational concepts in quantum theory. Here, we attempt such an analysis through quantum set theory (QST. In this paper, we develop quantum set theory based on quantum logics with those three conditionals, each of which defines different quantum logical truth value assignment. We show that those three models satisfy the transfer principle of the same form to determine the quantum logical truth values of theorems of the ZFC set theory. We also show that the reals in the model and the truth values of their equality are the same for those models. Interestingly, however, the order relation between quantum reals significantly depends on the underlying conditionals. We characterize the operational meanings of those order relations in terms of joint probability obtained by the successive projective measurements of arbitrary two observables. Those characterizations clearly show their individual features and will play a fundamental role in future applications to quantum physics.
Ihly, Rachelle
2014-01-01
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic s...
Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H. F.
2013-05-01
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.
Battle of the sexes game analysis using Yang-Baxter operator as quantum gate
López R., Juan M.
2012-06-01
The Battle of the Sexes game is analyzed from quantum game theory using quantum initial states as possible strategies for two players. Quantum circuits are presented as schemes of development proposing also the use of Yang-Baxter operators as quantum gates in the circuits. This formalism is implemented using a Computer Algebra Software (CAS) due to its complex and long mathematical treatment. Payoff matrices of the players are given as the results for each case shown. Biology and finances applications are also proposed.
A quantum switching architecture on the basis of limited nonlocal operation
Institute of Scientific and Technical Information of China (English)
JIANG Min; ZHANG Zeng-ke; DONG Dao-yi
2006-01-01
Quantum information system is fragile to be disturbed by the external environment. Quantum switching architecture is one of the promising schemes for transferring input quantum data to its destination port substituted for fully connected quantum networks. Since at present, interactions between the qubits are limited to a small number of neighboring qubits, one novel approach was extended, and the improved architecture was further demonstrated under limited nonlocal operation. The performance evaluation shows that the whole architecture with improved control module can achieve a time complexity of O(n2) and will be more feasible for physical realization.
A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures
Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe
2014-10-01
Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like "Alice knows that Bob does not understand that π is irrational" as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators ( to understand, to know…) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of "memorizing and retrieving information" can be formally represented, in this framework, by using a quantum teleportation phenomenon.
Non-adiabatic holonomy operators in classical and quantum completely integrable systems
Giachetta, G; Sardanashvily, G
2002-01-01
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized Berry's phase factor), without any adiabatic approximation.
Das, Ashok
2016-01-01
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter $\\sigma\\,(0\\leq\\sigma\\leq\\beta)$. We point out new features which arise when $\\sigma\
Modified SQUID Operator Equation for a Single-Qubit Structure Coupled to a Quantum Resonator
Institute of Scientific and Technical Information of China (English)
LIANG Bao-Long; WANG Ji-Suo; FAN Hong-Yi; MENG Xiang-Guo
2008-01-01
Role of self-inductance in superconducting quantum interference device (SQUID) charge qubit is considered. It is found that when an SQUID charge qubit is coupled to a quantum LC resonator, the SQUID voltage operator equation is modified in accompanying with the modification of operator Faraday equation describing the inductance. It is shown that when the extra energy is applied to the junction, the mean phase will be squeezed according to a damping factor.
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2006-01-01
The annihilation-creation operators $a^{(\\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\\pm)}$ are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the `discrete' quantum mechanics.
Noon, Abbas; Kadry, Seifedine
2011-01-01
Round Robin, considered as the most widely adopted CPU scheduling algorithm, undergoes severe problems directly related to quantum size. If time quantum chosen is too large, the response time of the processes is considered too high. On the other hand, if this quantum is too small, it increases the overhead of the CPU. In this paper, we propose a new algorithm, called AN, based on a new approach called dynamic-time-quantum; the idea of this approach is to make the operating systems adjusts the time quantum according to the burst time of the set of waiting processes in the ready queue. Based on the simulations and experiments, we show that the new proposed algorithm solves the fixed time quantum problem and increases the performance of Round Robin.
Quantum Field Theory: From Operators to Path Integrals
Huang, Kerson
1998-07-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
Frenkel, Edward
2016-01-01
We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra U_q(g^) introduced in [HJ]. This system was discovered in [MRV1, MRV2], where it was shown that solutions of this system can be attached to certain affine opers for the Langlands dual affine Kac-Moody algebra of g^, introduced in [FF5]. Together with the results of [BLZ3, BHK], which enable one to associate quantum g^-KdV Hamiltonians to representations from the category O, this provides strong evidence for the conjecture of [FF5] linking the spectra of quantum g^-KdV Hamiltonians and affine opers for the Langlands dual affine algebra. As a bonus, we obtain a direct and uniform proof of the Bethe Ansatz equations for a large class of quantum integrable models associated to arbitrary untwisted quantum affine algebras, under a mild genericity condition.
Quantum Mechanical Version of z-Transform Related to Eigenkets of Boson Creation Operator
Institute of Scientific and Technical Information of China (English)
FANHong-Yi; FULiang; A.Wiinsche
2004-01-01
Using the completeness relation composed of the coherent state and of the eigenket of bosonic creation operator, we establish a one-to-one correspondence between the z-transform and the quantum-mechanical transform from the representation by number states |n) to the representation by coherent states |(z)) (Bargmann representation).In this way, the quantum-mechanical version of the various properties of z-transform are obtained and the operators for embodying these properties in the Fock space are derived, which may find applications in quantum states engineering.
Quantum field theory from operators to path integrals
Huang, Kerson
1998-01-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained
Actively Secure Two-Party Evaluation of Any Quantum Operation
DEFF Research Database (Denmark)
Dupuis, Frédéric; Nielsen, Jesper Buus; Salvail, Louis
2012-01-01
We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map , given as a quantum circuit, upon their joint quantum input state . Our protocol leaks no more to any active adversary than an ideal ...... functionality for provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4]....
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
Nanopatterned Quantum Dot Lasers for High Speed, High Efficiency, Operation
2015-04-27
SUBTITLE 13. SUPPLEMENTARY NOTES 12. DISTRIBUTION AVAILIBILITY STATEMENT 6. AUTHORS 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES 15. SUBJECT TERMS ...growth using metalorganic chemical vapor deposition (MOCVD). These methods allowed us to realize quantum dot active regions in which the injected carriers...temperature sensitivity , commonly observed in self-assembled QD lasers2. An alternate approach to SK QD formation is the use of nanopatterning with
High-fidelity gate operations for quantum computing beyond dephasing time limits
Souza, Alexandre M.; Sarthour, Roberto S.; Oliveira, Ivan S.; Suter, Dieter
2015-12-01
The implementation of quantum gates with fidelities that exceed the threshold for reliable quantum computing requires robust gates whose performance is not limited by the precision of the available control fields. The performance of these gates also should not be affected by the noisy environment of the quantum register. Here we use randomized benchmarking of quantum gate operations to compare the performance of different families of gates that compensate errors in the control field amplitudes and decouple the system from the environmental noise. We obtain average fidelities of up to 99.8%, which exceeds the threshold value for some quantum error correction schemes as well as the expected limit from the dephasing induced by the environment.
Fermionic quantum operations: a computational framework I. Basic invariance properties
Lakos, Gyula
2015-01-01
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ operations ($n=2$) are reflected in their formal power series expansions.
Note: A hand-held high-Tc superconducting quantum interference device operating without shielding.
He, D F
2011-02-01
By improving the compensation circuit, a hand-held high-Tc rf superconducting quantum interference devices (SQUID) system was developed. It could operate well when moving in unshielded environment. To check the operation, it was used to do eddy-current testing by hand moving the SQUID, and the artificial defect under 6 mm aluminum plate could be successfully detected in shielded environment.
Photonic quantum digital signatures operating over kilometer ranges in installed optical fiber
Collins, Robert J.; Fujiwara, Mikio; Amiri, Ryan; Honjo, Toshimori; Shimizu, Kaoru; Tamaki, Kiyoshi; Takeoka, Masahiro; Andersson, Erika; Buller, Gerald S.; Sasaki, Masahide
2016-10-01
The security of electronic communications is a topic that has gained noteworthy public interest in recent years. As a result, there is an increasing public recognition of the existence and importance of mathematically based approaches to digital security. Many of these implement digital signatures to ensure that a malicious party has not tampered with the message in transit, that a legitimate receiver can validate the identity of the signer and that messages are transferable. The security of most digital signature schemes relies on the assumed computational difficulty of solving certain mathematical problems. However, reports in the media have shown that certain implementations of such signature schemes are vulnerable to algorithmic breakthroughs and emerging quantum processing technologies. Indeed, even without quantum processors, the possibility remains that classical algorithmic breakthroughs will render these schemes insecure. There is ongoing research into information-theoretically secure signature schemes, where the security is guaranteed against an attacker with arbitrary computational resources. One such approach is quantum digital signatures. Quantum signature schemes can be made information-theoretically secure based on the laws of quantum mechanics while comparable classical protocols require additional resources such as anonymous broadcast and/or a trusted authority. Previously, most early demonstrations of quantum digital signatures required dedicated single-purpose hardware and operated over restricted ranges in a laboratory environment. Here, for the first time, we present a demonstration of quantum digital signatures conducted over several kilometers of installed optical fiber. The system reported here operates at a higher signature generation rate than previous fiber systems.
Secure Quantum Key Distribution Network with Bell States and Local Unitary Operations
Institute of Scientific and Technical Information of China (English)
LI Chun-Yan; ZHOU Hong-Yu; WANG Yan; DENG Fu-Guo
2005-01-01
@@ We propose a theoretical scheme for secure quantum key distribution network following the ideas in quantum dense coding. In this scheme, the server of the network provides the service for preparing and measuring the Bell states,and the users encode the states with local unitary operations. For preventing the server from eavesdropping, we design a decoy when the particle is transmitted between the users. The scheme has high capacity as one particle carries two bits of information and its efficiency for qubits approaches 100%. Moreover, it is unnecessary for the users to store the quantum states, which makes this scheme more convenient in applications than others.
An arbitrated quantum signature protocol based on the chained CNOT operations encryption
Li, Feng-Guang; Shi, Jian-Hong
2015-06-01
At present, the encryption scheme used by most arbitrated quantum signature (AQS) protocols is quantum one-time pad (QOTP) which encrypts data qubit by qubit. Though QOTP can achieve high security for data encryption, it is not suitable for AQS. There are many attacks on AQS using QOTP. In this paper, we propose an AQS protocol based on another encryption scheme called the chained CNOT operations, which encrypts quantum message ensemble. Our protocol preserves all merits in the similar AQS schemes and has better security. Security analysis shows that our protocol cannot be forged and disavowed under the existing attacks.
q-differential operator representation of the quantum superalgebra Uq(sl(M+1|N+1))
Kimura, K
1996-01-01
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag manifold. This realization provides us with a guide to construct the free field realization for the quantum affine superalgebra Uq^(sl(M+1|N+1)) at arbitrary level.
Characteristic operator functions for quantum input-plant-output models and coherent control
Gough, John E.
2015-01-01
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entries that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.
Quantum dynamics for classical systems with applications of the number operator
Bagarello, Fabio
2013-01-01
Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a uniqu...
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Dolfi, Michele, E-mail: dolfim@phys.ethz.ch; Troyer, Matthias, E-mail: troyer@phys.ethz.ch [ETH Zürich, Institute of Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation
Kalita, Gunajit; Saikia, Navajit
2016-10-01
The futuristic computing is desired to be more power full with low-power consumption. That is why quantum computing has been a key area of research for quite some time and is getting more and more attention. Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times. Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance. In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer. The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations. The quantum costs of these designs are comparable. Many of the implemented micro-operations are not seen in previous literatures. The performances of the proposed circuits are compared with existing designs wherever available.
Explicit expressions of quantum mechanical rotation operators for spins 1 to 2
Kocakoç, Mehpeyker; Tapramaz, Recep
2016-03-01
Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.
Bunao, Joseph
2016-01-01
This study considers the operator $\\hat{T}$ corresponding to the classical spacetime four-volume $T$ of a finite patch of spacetime in the context of Unimodular Loop Quantum Cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since $T$ is canonically conjugate to the cosmological "constant" $\\Lambda$, the operator $\\hat{T}$ is constructed by solving its canonical commutation relation with $\\hat{\\Lambda}$ - the operator corresponding to $\\Lambda$. %This is done by expanding $\\hat{T}$ in terms of Bender-Dunne-like basis operators $\\hat{T}_{m,n}$ and solving for the expansion coefficients. This conjugacy, along with the action of $\\hat{T}$ on definite volume states reducing to $T$, allows us to interpret that $\\hat{T}$ is indeed a quantum spacetime four-volume operator. The eigenstates $\\Phi_{\\tau}$ are calculated and, considering $\\tau\\in\\mathbb{R}$, we find that the $\\Phi_{\\tau}$'s are normalizable suggesting that the real line $\\mathbb{R}$ is in the discret...
Marinelli, Dimitri; Aquilanti, Vincenzo; Anderson, Roger W; Bitencourt, Ana Carla P; Ragni, Mirco
2014-01-01
A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Höhn, Philipp A.; Müller, Markus P.
2016-06-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest, within a much simpler setting, that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distinct laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are ‘enough’ observables that can be measured universally on several different quantum systems, we show that the observers’ descriptions are related by an element of the orthochronous Lorentz group {{{O}}}+(3,1), together with a global scaling factor. Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern-Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.
Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED.
Hua, Ming; Tao, Ming-Jie; Deng, Fu-Guo
2015-03-19
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
Application of generalized operator representation in the time evolution of quantum systems
He, Rui; Liu, Xiangyuan; Song, Jun
2016-10-01
We have systematically explored the application of generalized operator representation including P-, W-, and Husimi representation in the time evolution of quantum systems. In particular, by using the method of differentiation within an ordered product of operators, we give the normally and antinormally ordered forms of the integral kernels of Husimi operator representations and its corresponding formulations. By making use of the generalized operator representation, we transform exponentially complex operator equations into tractable phase-space equations. As a simple application, the time evolution equation of Husimi function in the amplitude dissipative channel is clearly obtained.
Roga, W.; Spehner, D.; Illuminati, F.
2016-06-01
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Yang, Jinsong; Ma, Yongge
2017-04-01
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)
2017-04-15
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Hoehn, Philipp A
2015-01-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest within a much simpler setting that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distant laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are "enough" observables that can be measured jointly on different types of systems, we show that the observers' descriptions are related by an element of the Lorentz group O^+(3,1), together with a global ...
Ou, Congjie; Chamberlin, Ralph V.; Abe, Sumiyoshi
2017-01-01
The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, the following question is posed: in a quantum open system with a time-dependent Hamiltonian such as a subsystem in contact with the heat bath, what is the corresponding Lindblad equation for the quantum state that keeps the internal energy of the subsystem constant in time? This issue is of importance in realizing quasi-stationary states of open systems such as quantum circuits and batteries. As an illustrative example, the time-dependent harmonic oscillator is analyzed. It is shown that the Lindbladian operator is uniquely determined with the help of a Lie-algebraic structure, and the time derivative of the von Neumann entropy is shown to be nonnegative if the curvature of the harmonic potential monotonically decreases in time.
Generalized space and linear momentum operators in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Costa, Bruno G. da, E-mail: bruno.costa@ifsertao-pe.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Campus Petrolina, BR 407, km 08, 56314-520 Petrolina, Pernambuco (Brazil); Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil); Borges, Ernesto P., E-mail: ernesto@ufba.br [Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil)
2014-06-15
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics
Coutinho, F. A. B.; Amaku, M.
2009-01-01
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…
Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics
Coutinho, F. A. B.; Amaku, M.
2009-01-01
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…
On $q$-normal operators and quantum complex plane
Cimpri\\vc, Jaka; Schmüdgen, Konrad
2011-01-01
For $q>0$ let $\\cA$ denote the unital $\\ast$-algebra with generator $x$ and defining relation $xx^\\ast=qxx^\\ast$. Based on this algebra we study $q$-normal operators, the complex $q$-moment problem, positive elements and sums of squares.
Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
Dittrich, Bianca
2007-01-01
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck scale geometry in LQG is discontinuous rather than smooth. However, there is no rigorous proof thereof at present, because the afore mentioned operators are not gauge invariant, they do not commute with the quantum constraints. The relational formalism in the incarnation of Rovelli's partial and complete observables provides a possible mechanism for turning a non gauge invariant operator into a gauge invariant one. In this paper we investigate whether the spectrum of such a physical, that is gauge invariant, observable can be predicted from the spectrum of the corresponding gauge variant observables. We will not do this in full LQG but rather consider much simpler examples where field theoretical complications are absent. We find, even in those simpler cases, that kinematical discreteness of the spectrum does not n...
Far-infrared quantum cascade lasers operating in AlAs phonon Reststrahlen band
Ohtani, K; Süess, M J; Faist, J; Andrews, A M; Zederbauer, T; Detz, H; Schrenk, W; Strasser, G
2016-01-01
We report on the operation of a double metal waveguide far-infrared quantum cascade laser emitting at 28 $\\mu$m, corresponding to the AlAs-like phonon Reststrahlen band. To avoid absorption by AlAs-like optical phonons, the Al-free group-V alloy GaAs$_{0.51}$Sb$_{0.49}$ is used as a barrier layer in the bound-to-continuum based active region. Lasing occurs at a wavelength of 28.3 $\\mu$m, which is the longest wavelength among the quantum cascade lasers operating from mid-infrared to far-infrared. The threshold current density at 50 K is 5.5 kA/cm$^{2}$ and maximum operation temperature is 175 K. We also discuss the feasibility that operation wavelength cover the whole spectral range bridging between mid-infrared and terahertz by choosing suited group III-V materials.
Room Temperature Operation of a Buried Heterostructure Photonic Crystal Quantum Cascade Laser
Peretti, R; Wolf, J M; Bonzon, C; Süess, M J; Lourdudoss, S; Metaferia, W; Beck, M; Faist, J
2015-01-01
We demonstrated room temperature operation of deep etched photonic crystal quantum cascade laser emitting around 8.5 micron. We fabricated buried heterostructure photonic crystals, resulting in single mode laser emission on a high order slow Bloch modes of the photonic crystal, between high symmetry points of the Brillouin.
Construction of some Quantum Stochastic Operator Cocycles by the Semigroup Method
Indian Academy of Sciences (India)
J Martin Lindsay; Stephen J Wills
2006-11-01
A new method for the construction of Fock-adapted quantum stochastic operator cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter–Kato theorem and a recent characterisation of such cocycles in terms of an associated family of contraction semigroups.
The Fermionic Signature Operator and Quantum States in Rindler Space-Time
Finster, Felix; Röken, Christian
2016-01-01
The fermionic signature operator is constructed in Rindler space-time. It is shown to be an unbounded self-adjoint operator on the Hilbert space of solutions of the massive Dirac equation. In two-dimensional Rindler space-time, we prove that the resulting fermionic projector state coincides with the Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a covariant construction of general thermal states, in particular of the Unruh state. The fermionic signature operator is shown to be well-defined in asymptotically Rindler space-times. In four-dimensional Rindler space-time, our construction gives rise to new quantum states.
Stewart, Terrence C; Eliasmith, Chris
2013-06-01
Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).
A Scheme for Atomic Entangled States and Quantum Gate Operations in Cavity QED
Institute of Scientific and Technical Information of China (English)
LI Peng-Bo; GU Ying; GONG Qi-Huang; GUO Guang-Can
2009-01-01
We propose a scheme for controllably entangling the ground states of five-state W-type atoms confined in a cavity and realizing swap gate and phase gate operations.In this scheme the cavity is only virtually excited and the atomic excited states are almost not occupied,so the produced entangled states and quantum logic operations are very robust against the cavity decay and atomic spontaneous emission.
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Strauss, Y; Machnes, S; Horwitz, L P
2011-01-01
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.
Scheme for Remote Implementation of Partially Unknown Quantum Operation of Two Qubits in Cavity QED
Institute of Scientific and Technical Information of China (English)
QIU Liang; WANG An-Min
2008-01-01
By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An-Min Wang: Phys. Rev. A 74 (2006) 032317] with two-qubit Cnot gate and single qubit logic gates, we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.
Fan, Hong-yi; Lu, Hai-liang; Fan, Yue
2006-02-01
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., | q>mechanics are usually not commutative. Therefore, integrations over the operators of type |>mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.
BRST and anti-BRST operators for quantum linear algebra U{sub q}(gl(N))
Energy Technology Data Exchange (ETDEWEB)
Isaev, A.P. E-mail: isaevap@thsun1.jinr.ru; Ogievetsky, O.V. E-mail: isaevap@thsun1.jinr.ru
2001-09-01
For a quantum Lie algebra U{sub q}(gl(N)) we construct BRST, anti-BRST and Laplace operators. The (anti)commutator with the BRST operator defines the differential on the de Rham complex over the quantum group GL{sub q}(N). The Hodge decomposition theorem for this complex is formulated.
Renormalizing the kinetic energy operator in elementary quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail: coutinho@dim.fm.usp.br
2009-09-15
In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.
Bunao, J.
2017-02-01
This study considers the operator \\hat{T} corresponding to the classical spacetime four-volume \\tilde{T} (on-shell) of a finite patch of spacetime in the context of unimodular loop quantum cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological ‘constant’, the operator \\hat{T} is constructed by solving its canonical commutation relation with {\\hat Λ } —the operator corresponding to the classical cosmological constant on-shell {\\tilde Λ } . This conjugacy, along with the action of \\hat{T} on definite volume states reducing to \\tilde{T} , allows us to interpret that \\hat{T} is indeed a quantum spacetime four-volume operator. The discrete spectrum of \\hat{T} is calculated by considering the set of all τ’s where the eigenvalue equation has a solution {{ Φ }τ} in the domain of \\hat{T} . It turns out that, upon assigning the maximal domain D≤ft(\\hat{T}\\right) to \\hat{T} , we have {{ Φ }τ}\\in D≤ft(\\hat{T}\\right) for all τ \\in {C} so that the spectrum of \\hat{T} is purely discrete and is the entire complex plane. A family of operators {{\\hat{T}}≤ft({{b0},{φ0}\\right)}} was also considered as possible self-adjoint versions of \\hat{T} . They represent the restrictions of \\hat{T} on their respective domains D≤ft({{\\hat{T}}≤ft({{b0},{φ0}\\right)}}\\right) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers {τm} for m=0,+/- 1,+/- 2,... .
Chitambar, Eric; Gour, Gilad
2016-07-01
Considerable work has recently been directed toward developing resource theories of quantum coherence. In this Letter, we establish a criterion of physical consistency for any resource theory. This criterion requires that all free operations in a given resource theory be implementable by a unitary evolution and projective measurement that are both free operations in an extended resource theory. We show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations as a natural generalization of the physically consistent operations. Necessary and sufficient conditions are derived for the convertibility of qubit states using dephasing-covariant operations, and we show that these conditions also hold for other well-known classes of incoherent operations.
Chitambar, Eric; Gour, Gilad
2016-07-15
Considerable work has recently been directed toward developing resource theories of quantum coherence. In this Letter, we establish a criterion of physical consistency for any resource theory. This criterion requires that all free operations in a given resource theory be implementable by a unitary evolution and projective measurement that are both free operations in an extended resource theory. We show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations as a natural generalization of the physically consistent operations. Necessary and sufficient conditions are derived for the convertibility of qubit states using dephasing-covariant operations, and we show that these conditions also hold for other well-known classes of incoherent operations.
Jackson, John David
2006-01-01
Advanced undergraduates and graduate students studying quantum mechanics will find this text a valuable guide to mathematical methods. Emphasizing the unity of a variety of different techniques, it is enduringly relevant to many physical systems outside the domain of quantum theory.Concise in its presentation, this text covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. Appendixes offer useful information on Bessel functions and Legendre functions and spherical harmonics.
Active mode locking of quantum cascade lasers operating in external ring cavity
Revin, D G; Wang, Y; Cockburn, J W; Belyanin, A
2015-01-01
Stable ultrashort light pulses and frequency combs generated by mode-locked lasers have many important applications including high-resolution spectroscopy, fast chemical detection and identification, studies of ultrafast processes, and laser metrology. While compact mode-locked lasers emitting in the visible and near infrared range have revolutionized photonic technologies, the systems operating in the mid-infrared range where most gases have their strong absorption lines, are bulky and expensive and rely on nonlinear frequency down-conversion. Quantum cascade lasers are the most powerful and versatile compact light sources in the mid-infrared range, yet achieving their mode locked operation remains a challenge despite dedicated effort. Here we report the first demonstration of active mode locking of an external-cavity quantum cascade laser. The laser operates in the mode-locked regime at room temperature and over the full dynamic range of injection currents of a standard commercial laser chip.
Uzdin, Raam
2016-08-01
Collective behavior, where a set of elements interact and generate effects that are beyond the reach of the individual noninteracting elements, is always of great interest in physics. Quantum collective effects that have no classical analog are even more intriguing. In this work, we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines, the individual units operate in a stochastic, nonquantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together, these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines, we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and then becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine, we introduce the "entropy-pollution" measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.
On the discrete spectrum of the Dirac operator on bent chain quantum graph
Directory of Open Access Journals (Sweden)
Belov Michail
2017-01-01
Full Text Available We study Dirac operators on an infinite quantum graph of a bent chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ ℝ. We are interested in the discrete spectrum of the corresponding Hamiltonian. It can be non-empty due to a local (geometrical perturbation of the corresponding infinite chain of rings. The quantum graph of analogous geometry with the Schrodinger operator on the edges was considered by Duclos, Exner and Turek in 2008. They showed that the absence of δ-couplings at vertices (i.e. the Kirchhoff condition at the vertices lead to the absence of eigenvalues. We consider the relativistic particle (the Dirac operator instead of the Schrodinger one but the result is analogous. Quantum graphs of such type are suitable for description of grapheme-based nanostructures. It is established that the negativity of α is the necessary and sufficient condition for the existence of eigenvalues of the Dirac operator (i.e. the discrete spectrum of the Hamiltonian in this case is not empty. The continuous spectrum of the Hamiltonian for bent chain graph coincides with that for the corresponding straight infinite chain. Conditions for appearance of more than one eigenvalue are obtained. It is related to the bending angle. The investigation is based on the transfer-matrix approach. It allows one to reduce the problem to an algebraic task. δ-couplings was introduced by the operator extensions theory method.
Khrennikov, Andrei
2016-09-01
We represent Born's rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born's rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.
Reveal non-Markovianity of open quantum systems via local operations
Yang, Huan; Chen, Yanbei
2011-01-01
Non-Markovianity, as an important feature of general open quantum systems, is usually difficult to quantify with limited knowledge of how the plant that we are interested in interacts with its environment-the bath. It often happens that the reduced dynamics of the plant attached to a non-Markovian bath becomes indistinguishable from the one with a Markovian bath, if we left the entire system freely evolve. Here we show that non-Markovianity can be revealed via applying local unitary operations on the plant-they will influence the plant evolution at later times due to memory of the bath. This not only provides a new criterion for non-Markovianity, but also sheds light on protecting and recovering quantum coherence in non-Markovian systems, which will be useful for quantum-information processing.
Memristive operation mode of a site-controlled quantum dot floating gate transistor
Energy Technology Data Exchange (ETDEWEB)
Maier, P., E-mail: patrick.maier@physik.uni-wuerzburg.de; Hartmann, F.; Mauder, T.; Emmerling, M.; Schneider, C.; Kamp, M.; Worschech, L. [Technische Physik, Physikalisches Institut, Wilhelm Conrad Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); Höfling, S. [Technische Physik, Physikalisches Institut, Wilhelm Conrad Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS (United Kingdom)
2015-05-18
We have realized a floating gate transistor based on a GaAs/AlGaAs heterostructure with site-controlled InAs quantum dots. By short-circuiting the source contact with the lateral gates and performing closed voltage sweep cycles, we observe a memristive operation mode with pinched hysteresis loops and two clearly distinguishable conductive states. The conductance depends on the quantum dot charge which can be altered in a controllable manner by the voltage value and time interval spent in the charging region. The quantum dot memristor has the potential to realize artificial synapses in a state-of-the-art opto-electronic semiconductor platform by charge localization and Coulomb coupling.
Quantum dynamics of a macroscopic magnet operating as an environment of a mechanical oscillator
Foti, C.; Cuccoli, A.; Verrucchi, P.
2016-12-01
We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-1/2 particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin S constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-S limit. We find an insightful expression for the propagator of the whole system, where we identify an effective "back-action" term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.
Quantum-optical description of losses in ring resonators based on field-operator transformations
Alsing, Paul M.; Hach, Edwin E.; Tison, Christopher C.; Smith, A. Matthew
2017-05-01
In this work we examine loss in ring resonator networks from an operator valued phasor addition approach which considers the multiple transmission and cross coupling paths of a quantum field traversing a ring resonator coupled to one or two external waveguide buses. We demonstrate the consistency of our approach by the preservation of the operator commutation relation of the out-coupled bus mode. We compare our results to those obtained from the conventional quantum Langevin approach which introduces noise operators in addition to the quantum Heisenberg equations in order to preserve commutation relations in the presence of loss. It is shown that the two expressions agree in the neighborhood of a cavity resonance where the Langevin approach is applicable, whereas the operator valued phasor addition expression we derive is more general, remaining valid far from resonances. In addition, we examine the effects of internal and coupling losses on the Hong-Ou-Mandel manifold discussed in Hach et al. [Phys. Rev. A 89, 043805 (2014), 10.1103/PhysRevA.89.043805] that generalizes the destructive interference of two incident photons interfering on a 50:50 beam splitter (HOM effect) to the case of an add-drop double bus ring resonator.
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hugo [Tuebingen Univ. (Germany). Inst. fuer Theoretische Physik
2012-11-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Quantum Exchange Algebra and Exact Operator Solution of $A_{2}$-Toda Field Theory
Takimoto, Y; Kurokawa, H; Fujiwara, T
1999-01-01
Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is automatically guaranteed by the locality. Quantum Toda theories are investigated by applying the method of free field quantization. We give Toda exponential operators associated with fundamental weight vectors as bilinear forms of chiral fields satisfying characteristic quantum exchange algebra. It is shown that the locality leads to nontrivial relations among the ${\\cal R}$-matrix and the expansion coefficients of the exponential operators. The Toda exponentials are obtained for $A_2$-system by extending the algebraic method developed for Liouville theory. The canonical commutation relations and the operatorial field equations are also examined.
Institute of Scientific and Technical Information of China (English)
HAN Lian-Fang; CHEN Yue-Ming; YUAN Hao
2009-01-01
We propose a deterministic quantum secure direct communication protocol by using dense coding.The two check photon sequences are used to check the securities of the channels between the message sender and the receiver.The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced.Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel.In addition, the scheme is still secure in noise channel.Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.
Rapid single-flux-quantum circuits for low noise mK operation
Intiso, Samuel; Pekola, Jukka; Savin, Alexander; Devyatov, Ygor; Kidiyarova-Shevchenko, Anna
2006-05-01
Rapid single-flux-quantum (RSFQ) technology has been proposed as control electronics for superconducting quantum bits because of the material and working temperature compatibility. In this work, we consider practical aspects of RSFQ circuit design for low noise low power operation. At the working temperature of 20 mK and operational frequency of 2 GHz, dissipated power per junction is reduced to 25 pW by using 6 µA critical current junctions available at the Hypres and VTT low Jc fabrication process. To limit phonon temperature to 30 mK, a maximum of 40 junctions can be placed on a 5 mm × 5 mm chip. Electron temperature in resistive shunts of Josephson junctions is minimized by use of cooling fins, giving minimum electron temperatures of about 150 mK for the Hypres process and 70 mK for the VTT process.
A gravitational wave observatory operating beyond the quantum shot-noise limit
Ligo Scientific Collaboration; Abadie, J.; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M.; Adams, C.; Adhikari, R.; Affeldt, C.; Allen, B.; Allen, G. S.; Amador Ceron, E.; Amariutei, D.; Amin, R. S.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Arain, M. A.; Araya, M. C.; Aston, S. M.; Atkinson, D.; Aufmuth, P.; Aulbert, C.; Aylott, B. E.; Babak, S.; Baker, P.; Ballmer, S.; Barker, D.; Barr, B.; Barriga, P.; Barsotti, L.; Barton, M. A.; Bartos, I.; Bassiri, R.; Bastarrika, M.; Batch, J.; Bauchrowitz, J.; Behnke, B.; Bell, A. S.; Belopolski, I.; Benacquista, M.; Berliner, J. M.; Bertolini, A.; Betzwieser, J.; Beveridge, N.; Beyersdorf, P. T.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Biswas, R.; Black, E.; Blackburn, J. K.; Blackburn, L.; Blair, D.; Bland, B.; Bock, O.; Bodiya, T. P.; Bogan, C.; Bondarescu, R.; Bork, R.; Born, M.; Bose, S.; Brady, P. R.; Braginsky, V. B.; Brau, J. E.; Breyer, J.; Bridges, D. O.; Brinkmann, M.; Britzger, M.; Brooks, A. F.; Brown, D. A.; Brummitt, A.; Buonanno, A.; Burguet-Castell, J.; Burmeister, O.; Byer, R. L.; Cadonati, L.; Camp, J. B.; Campsie, P.; Cannizzo, J.; Cannon, K.; Cao, J.; Capano, C. D.; Caride, S.; Caudill, S.; Cavagliá, M.; Cepeda, C.; Chalermsongsak, T.; Chalkley, E.; Charlton, P.; Chelkowski, S.; Chen, Y.; Christensen, N.; Cho, H.; Chua, S. S. Y.; Chung, S.; Chung, C. T. Y.; Ciani, G.; Clara, F.; Clark, D. E.; Clark, J.; Clayton, J. H.; Conte, R.; Cook, D.; Corbitt, T. R.; Cordier, M.; Cornish, N.; Corsi, A.; Costa, C. A.; Coughlin, M.; Couvares, P.; Coward, D. M.; Coyne, D. C.; Creighton, J. D. E.; Creighton, T. D.; Cruise, A. M.; Cumming, A.; Cunningham, L.; Cutler, R. M.; Dahl, K.; Danilishin, S. L.; Dannenberg, R.; Danzmann, K.; Daudert, B.; Daveloza, H.; Davies, G.; Daw, E. J.; Dayanga, T.; Debra, D.; Degallaix, J.; Dent, T.; Dergachev, V.; Derosa, R.; Desalvo, R.; Dhurandhar, S.; Diguglielmo, J.; di Palma, I.; Díaz, M.; Donovan, F.; Dooley, K. L.; Dorsher, S.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Dumas, J.-C.; Dwyer, S.; Eberle, T.; Edgar, M.; Edwards, M.; Effler, A.; Ehrens, P.; Engel, R.; Etzel, T.; Evans, K.; Evans, M.; Evans, T.; Factourovich, M.; Fairhurst, S.; Fan, Y.; Farr, B. F.; Farr, W.; Fazi, D.; Fehrmann, H.; Feldbaum, D.; Finn, L. S.; Fisher, R. P.; Flanigan, M.; Foley, S.; Forsi, E.; Fotopoulos, N.; Frede, M.; Frei, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Friedrich, D.; Fritschel, P.; Frolov, V. V.; Fulda, P. J.; Fyffe, M.; Ganija, M. R.; Garcia, J.; Garofoli, J. A.; Geng, R.; Gergely, L. Á.; Gholami, I.; Ghosh, S.; Giaime, J. A.; Giampanis, S.; Giardina, K. D.; Gill, C.; Goetz, E.; Goggin, L. M.; González, G.; Gorodetsky, M. L.; Goßler, S.; Graef, C.; Grant, A.; Gras, S.; Gray, C.; Gray, N.; Greenhalgh, R. J. S.; Gretarsson, A. M.; Grosso, R.; Grote, H.; Grunewald, S.; Guido, C.; Gupta, R.; Gustafson, E. K.; Gustafson, R.; Ha, T.; Hage, B.; Hallam, J. M.; Hammer, D.; Hammond, G.; Hanks, J.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G. M.; Harry, I. W.; Harstad, E. D.; Hartman, M. T.; Haughian, K.; Hayama, K.; Heefner, J.; Heintze, M. C.; Hendry, M. A.; Heng, I. S.; Heptonstall, A. W.; Herrera, V.; Hewitson, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Holt, K.; Hong, T.; Hooper, S.; Hosken, D. J.; Hough, J.; Howell, E. J.; Hughey, B.; Huynh-Dinh, T.; Husa, S.; Huttner, S. H.; Ingram, D. R.; Inta, R.; Isogai, T.; Ivanov, A.; Izumi, K.; Jacobson, M.; Jang, H.; Johnson, W. W.; Jones, D. I.; Jones, G.; Jones, R.; Ju, L.; Kalmus, P.; Kalogera, V.; Kamaretsos, I.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Katsavounidis, E.; Katzman, W.; Kaufer, H.; Kawabe, K.; Kawamura, S.; Kawazoe, F.; Kells, W.; Keppel, D. G.; Keresztes, Z.; Khalaidovski, A.; Khalili, F. Y.; Khazanov, E. A.; Kim, B.; Kim, C.; Kim, D.; Kim, H.; Kim, K.; Kim, N.; Kim, Y.-M.; King, P. J.; Kinsey, M.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kokeyama, K.; Kondrashov, V.; Kopparapu, R.; Koranda, S.; Korth, W. Z.; Kozak, D.; Kringel, V.; Krishnamurthy, S.; Krishnan, B.; Kuehn, G.; Kumar, R.; Kwee, P.; Lam, P. K.; Landry, M.; Lang, M.; Lantz, B.; Lastzka, N.; Lawrie, C.; Lazzarini, A.; Leaci, P.; Lee, C. H.; Lee, H. M.; Leindecker, N.; Leong, J. R.; Leonor, I.; Li, J.; Lindquist, P. E.; Lockerbie, N. A.; Lodhia, D.; Lormand, M.; Luan, J.; Lubinski, M.; Lück, H.; Lundgren, A. P.; MacDonald, E.; Machenschalk, B.; Macinnis, M.; MacLeod, D. M.; Mageswaran, M.; Mailand, K.; Mandel, I.; Mandic, V.; Marandi, A.; Márka, S.; Márka, Z.; Markosyan, A.; Maros, E.; Martin, I. W.; Martin, R. M.; Marx, J. N.; Mason, K.; Matichard, F.; Matone, L.; Matzner, R. A.; Mavalvala, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McIntyre, G.; McIver, J.; McKechan, D. J. A.; Meadors, G. D.; Mehmet, M.; Meier, T.; Melatos, A.; Melissinos, A. C.; Mendell, G.; Menendez, D.
2011-12-01
Around the globe several observatories are seeking the first direct detection of gravitational waves (GWs). These waves are predicted by Einstein's general theory of relativity and are generated, for example, by black-hole binary systems. Present GW detectors are Michelson-type kilometre-scale laser interferometers measuring the distance changes between mirrors suspended in vacuum. The sensitivity of these detectors at frequencies above several hundred hertz is limited by the vacuum (zero-point) fluctuations of the electromagnetic field. A quantum technology--the injection of squeezed light--offers a solution to this problem. Here we demonstrate the squeezed-light enhancement of GEO600, which will be the GW observatory operated by the LIGO Scientific Collaboration in its search for GWs for the next 3-4 years. GEO600 now operates with its best ever sensitivity, which proves the usefulness of quantum entanglement and the qualification of squeezed light as a key technology for future GW astronomy.
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
Institute of Scientific and Technical Information of China (English)
刘当婷; 田野; 赵士平; 任育峰; 陈赓华
2015-01-01
We discuss a simple relation between the input and output signals of a superconducting quantum interference device magnetometer operating in flux locked mode in a cosine curve approximation. According to this relation, an original fast input signal can be easily retrieved from its distorted output response. This technique can be used in some areas such as sensitive and fast detection of magnetic or metallic grains in medicine and food security checking.
2008-01-01
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable potentials, the resulting Schr\\"odinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and conjecture that the same method can be ...
Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.
Chia, A; Tan, K C; Pawela, Ł; Kurzyński, P; Paterek, T; Kaszlikowski, D
2016-03-01
Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.
Room-temperature operation of mid-infrared surface-plasmon quantum cascade lasers
Bahriz, M.; Moreau, V.; Palomo, J.; Krysa, A. B.; Austin, D.; Cockburn, J. W.; Roberts, J. S.; Wilson, L. R.; Julien, F.; Colombelli, R.
2007-04-01
We report the pulsed, room-temperature operation of an InGaAs/AllnAs quantum cascade laser at an operating wavelength of ≈ 7.5 μm in which the optical mode is a surface-plasmon polariton excitation. The use of a silver-based electrical contact with reduced optical losses at the laser emission wavelength allows for a reduction of the laser threshold current by a factor of two relative to samples with a gold-based contact layer.
High Temperature Operation of 5.5μm Strain-Compensated Quantum Cascaded Lasers
Institute of Scientific and Technical Information of China (English)
LU Xiu-Zhen; LIU Feng-Qi; LIU Jun-Qi; JIN Peng; WANG Zhan-Guo
2005-01-01
@@ We develop 5.5-μm Inx Ga1-xAs/InyAl1-yAs strain-compensated quantum cascade lasers with InP and InGaAs cladding layers by using solid-source molecular-beam epitaxy. Pulse operation has been achieved up to 323K (50℃) for uncoated 20-μm-wide and 2-mm-long devices. These devices display an output power of 36mW with a duty cycle of 1% at room temperature. In continuous wave operation a record peak optical power of 10mW per facet has been measured at 83 K.
Continuous wave operation of quantum cascade lasers with frequency-shifted feedback
Energy Technology Data Exchange (ETDEWEB)
Lyakh, A., E-mail: arkadiy.lyakh@ucf.edu [Pranalytica, Inc., 1101 Colorado Ave., Santa Monica, CA 90401 (United States); NanoScience Technology Center, University of Central Florida, 12424 Research Pkwy, Orlando, FL 32826 (United States); College of Optics and Photonics, University of Central Florida, 304 Scorpius St, Orlando, FL 32826 (United States); Barron-Jimenez, R.; Dunayevskiy, I.; Go, R.; Tsvid, G.; Patel, C. Kumar N., E-mail: patel@pranalytica.com [Pranalytica, Inc., 1101 Colorado Ave., Santa Monica, CA 90401 (United States)
2016-01-15
Operation of continuous wave quantum cascade lasers with a frequency-shifted feedback provided by an acousto-optic modulator is reported. Measured linewidth of 1.7 cm{sup −1} for these devices, under CW operating conditions, was in a good agreement with predictions of a model based on frequency-shifted feedback seeded by spontaneous emission. Linewidth broadening was observed for short sweep times, consistent with sound wave grating period variation across the illuminated area on the acousto-optic modulator. Standoff detection capability of the AOM-based QCL setup was demonstrated for several solid materials.
Realization of the N(odd)-Dimensional Quantum Euclidean Space by Differential Operators
Institute of Scientific and Technical Information of China (English)
LI Yun; JING Si-Cong
2004-01-01
The quantum Euclidean space RNq is a kind of noncommutative space that is obtained from ordinary Euclidean space RN by deformation with parameter q. When N is odd, the structure of this space is similar to R3q.Motivated by realization ofR3q by differential operators in R3, we give such realization for R5q and R7q cases and generalize our results to RNq (N odd) in this paper, that is, we show that the algebra of RNq can be realized by differential operators acting on C∞ functions on undeformed space RN.
Institute of Scientific and Technical Information of China (English)
WANG Yi-Min; ZHOU Yan-Li; LIANG Lin-Mei; LI Cheng-Zu
2009-01-01
We propose a feasible scheme to achieve universal quantum gate operations in decoherence-free subspace with superconducting charge qubits placed in a microwave cavity.Single-logic-qubit gates can be realized with cavity assisted interaction, which possesses the advantages of unconventional geometric gate operation.The two-logic-qubit controlled-phase gate between subsystems can be constructed with the help of a variable electrostatic transformer, The collective decoherence can be successfully avoided in our well-designed system.Moreover, GHZ state for logical qubits can also be easily produced in this system.
Directory of Open Access Journals (Sweden)
Schnabel Roman
2013-08-01
Full Text Available This contribution reviews our recent progress on the generation of squeezed light [1], and also the recent squeezed-light enhancement of the gravitational wave detector GEO 600 [2]. GEO 600 is currently the only GW observatory operated by the LIGO Scientific Collaboration in its search for gravitational waves. With the help of squeezed states of light it now operates with its best ever sensitivity, which not only proves the qualification of squeezed light as a key technology for future gravitational wave astronomy but also the usefulness of quantum entanglement.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
New approach for anti-normally and normally ordering bosonic-operator functions in quantum optics
Xu, Shi-Min; Zhang, Yun-Hai; Xu, Xing-Lei; Li, Hong-Qi; Wang, Ji-Suo
2016-12-01
In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f(λQ̂ + νP̂) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations. Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2015AM025) and the Natural Science Foundation of Heze University, China (Grant No. XY14PY02).
Directory of Open Access Journals (Sweden)
D. H. Wu
2017-03-01
Full Text Available We demonstrate a surface grating coupled substrate emitting quantum cascade ring laser with high power room temperature continuous wave operation at 4.64 μm. A second order surface metal/semiconductor distributed-feedback grating is used for in-plane feedback and vertical out-coupling. A device with 400 μm radius ring cavity exhibits an output power of 202 mW in room temperature continuous wave operation. Single mode operation with a side mode suppression ratio of 25 dB is obtained along with a good linear tuning with temperature. The far field measurement exhibits a low divergent concentric ring beam pattern with a lobe separation of ∼0.34°, which indicates that the device operates in fundamental mode (n = 1.
Directory of Open Access Journals (Sweden)
Abbas Noon
2011-05-01
Full Text Available Round Robin, considered as the most widely adopted CPU scheduling algorithm, undergoes severe problems directly related to quantum size. If time quantum chosen is too large, the response time of the processes is considered too high. On the other hand, if this quantum is too small, it increases the overhead of the CPU. In this paper, we propose a new algorithm, called AN, based on a new approach called dynamic-time-quantum; the idea of this approach is to make the operating systems adjusts the time quantum according to the burst time of the set of waiting processes in the ready queue. Based on the simulations and experiments, we show that the new proposed algorithm solves the fixed time quantum problem and increases the performance of Round Robin.
Two-loop scale-invariant scalar potential and quantum effective operators
Energy Technology Data Exchange (ETDEWEB)
Ghilencea, D.M. [National Institute of Physics and Nuclear Engineering (IFIN-HH), Theoretical Physics Department, Bucharest (Romania); CERN, Theory Division, Geneva 23 (Switzerland); Lalak, Z.; Olszewski, P. [University of Warsaw, Faculty of Physics, Institute of Theoretical Physics, Warsaw (Poland)
2016-12-15
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a Higgs-like scalar φ in theories in which scale symmetry is broken only spontaneously by the dilaton (σ). Its VEV left angle σ right angle generates the DR subtraction scale (μ ∝ left angle σ right angle), which avoids the explicit scale symmetry breaking by traditional regularizations (where μ = fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking (μ = fixed scale). These operators have the form φ{sup 6}/σ{sup 2}, φ{sup 8}/σ{sup 4}, etc., which generate an infinite series of higher dimensional polynomial operators upon expansion about left angle σ right angle >> left angle φ right angle, where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions (∝ ε) between σ and φ that vanish in d = 4 but are required by classical scale invariance in d = 4 - 2ε. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with μ = fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking. (orig.)
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians
Patel, Apoorva; Priyadarsini, Anjani
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.
Two-loop scale-invariant scalar potential and quantum effective operators
Ghilencea, D.M.
2016-01-01
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...
Institute of Scientific and Technical Information of China (English)
WU Tao; LIU Jian-She; LI Zheng
2006-01-01
@@ Superconducting flux qubits with three Josephson junctions are promising candidates for the building blocks of a quantum computer. We have applied the imaginary time evolution method to study the model of this qubit accurately by calculating its wavefunctions and eigenenergies. Because such qubits are manipulated with magnetic lux microwave pulses, they might be irradiated into non-computational states, which is called the leakage effect.By the evolution of the density matrix of the qubit under either hard-shaped π-pulse or Gaussian-shaped π-pulse to carry out quantum NOT operation, it has been demonstrated that the leakage effect for a flux qubit is very small even for hard-shaped microwave pulses while Gaussian-shaped pulses may suppress the leakage effect to a negligible level.
Linear optics only allows every possible quantum operation for one photon or one port
Moyano-Fernández, Julio José; Garcia-Escartin, Juan Carlos
2017-01-01
We study the evolution of the quantum state of n photons in m different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators U that cannot be built with linear optics alone unless the number of photons or the number of modes is equal to one. The evolution for single photons can be controlled with the known realization of any unitary proved by Reck, Zeilinger, Bernstein and Bertani. The evolution for a single mode corresponds to the trivial evolution in a phase shifter. We analyze these two cases and prove that any other combination of the number of photons and modes produces a Hilbert state too large for the linear optics system to give any desired evolution.
Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\\hat{sl_N})$
Kojima, Takeo
2011-01-01
We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\\hat{sl_N})$. We call one of them the integral of motion ${\\cal G}_m$, $(m \\in {\\mathbb N})$ and the other the boundary transfer matrix $T_B(z)$, $(z \\in {\\mathbb C})$. The integral of motion ${\\cal G}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\\hat{sl_N})$ face model. We diagonalize the boundary transfer matrix $T_B(z)$ by using the free field realization of the elliptic quantum group, however diagonalization of the integral of motion ${\\cal G}_m$ is open problem even for the simplest case $U_{q,p}(\\hat{sl_2})$.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
Clawson, Savannah Ellen
2017-01-01
The quantum efficiency of a Burle 8850 photomultiplier tube with a potassium-caesium-antimony (bialkali) photocathode was determined by attenuating a 1 mW HeNe laser emitting at 633 nm and measuring the signal frequency when the laser was incident on the photomultiplier. A temperature range of 5 $^{\\circ}$C $-$ 20 $^{\\circ}$C was investigated and it was found that the quantum efficiency decreases with temperature, with the signal frequency decreasing at a faster rate than the dark current frequency. Therefore, it was concluded that it would not be beneficial to cool photomultiplier tubes operating in the visible spectrum for use in collinear laser spectroscopy due to a decreasing signal-to-noise ratio. The signal pulse height distribution was also analysed and found to be independent of temperature within the range investigated.
High-temperature operation of broadband bidirectional terahertz quantum-cascade lasers
Khanal, Sudeep; Gao, Liang; Zhao, Le; Reno, John L.; Kumar, Sushil
2016-09-01
Terahertz quantum cascade lasers (QCLs) with a broadband gain medium could play an important role for sensing and spectroscopy since then distributed-feedback schemes could be utilized to produce laser arrays on a single semiconductor chip with wide spectral coverage. QCLs can be designed to emit at two different frequencies when biased with opposing electrical polarities. Here, terahertz QCLs with bidirectional operation are developed to achieve broadband lasing from the same semiconductor chip. A three-well design scheme with shallow-well GaAs/Al0.10Ga0.90As superlattices is developed to achieve high-temperature operation for bidirectional QCLs. It is shown that shallow-well heterostructures lead to optimal quantum-transport in the superlattice for bidirectional operation compared to the prevalent GaAs/Al0.15Ga0.85As material system. Broadband lasing in the frequency range of 3.1-3.7 THz is demonstrated for one QCL design, which achieves maximum operating temperatures of 147 K and 128 K respectively in opposing polarities. Dual-color lasing with large frequency separation is demonstrated for a second QCL, that emits at ~3.7 THz and operates up to 121 K in one polarity, and at ~2.7 THz up to 105 K in the opposing polarity. These are the highest operating temperatures achieved for broadband terahertz QCLs at the respective emission frequencies, and could lead to commercial development of broadband terahertz laser arrays.
Non-compact groups, tensor operators and applications to quantum gravity
Sellaroli, Giuseppe
2016-01-01
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to generalise the Wigner-Eckart theorem to non-compact groups. The result relies on the knowledge of the recoupling theory between finite-dimensional and infinite-dimensional irreducible representations of the group; here the previously unconsidered cases of the 3D and 4D Lorentz groups are investigated in detail. As an application, the Wigner-Eckart theorem is used to generalise the Jordan-Schwinger representation of SU(2) to both groups, for all representation classes. Next, the results obtained for the 3D Lorentz group are applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the well-known spinorial approach used in the Euclidean case. Tensor operators are used to construct observables and to generalise the Hamiltonian constraint introduced by Bonzom and Liv...
Particle number conservation in quantum many-body simulations with matrix product operators
Muth, Dominik
2011-01-01
Incorporating conservation laws explicitly into Matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that often the entanglement imposed by the global constraint of fixed particle number is the limiting factor in the canonical ensemble.
Tunable single and dual mode operation of an external cavity quantum-dot injection laser
Energy Technology Data Exchange (ETDEWEB)
Biebersdorf, A [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Lingk, C [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); De Giorgi, M [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Feldmann, J [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Sacher, J [Sacher Lasertechnik GmbH, Hannah Arendt Strasse 3-7, D-35037 Marburg (Germany); Arzberger, M [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Ulbrich, C [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Boehm, G [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Amann, M-C [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Abstreiter, G [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany)
2003-08-21
We investigate quantum-dot (QD) lasers in an external cavity using Littrow and Littman configurations. Here, we report on a continuously tunable QD laser with a broad tuning range from 1047 to 1130 nm with high stability and efficient side mode suppression. The full-width at half-maximum of the laser line is 0.85 nm determined mainly by the quality of the external grating. This laser can be operated in a dual-mode modus, where the mode-spacing can be tuned continuously between 1.1 and 34 nm. Simultaneous emission of the two laser modes is shown by sum frequency generation experiments.
Extracting fundamental transverse mode operation in broad area quantum cascade lasers
Kaspi, R.; Luong, S.; Yang, C.; Lu, C.; Newell, T. C.; Bate, T.
2016-11-01
Power scaling in broad area quantum cascade lasers results in the operation of high order transverse modes with a far-field profile consisting of two lobes propagating at large angles relative to the optical axis. We report a method of suppressing the high order transverse modes that can extract the fundamental mode and provide emission along the optical axis. By generating a lateral constriction in the waveguide in the form of short trenches defined by the focused ion beam milling technique, we report broad area devices in which most of the power is contained in a near diffraction-limited beam that provides high brightness.
General Approach to Quantum Channel Impossibility by Local Operations and Classical Communication
Cohen, Scott M.
2017-01-01
We describe a general approach to proving the impossibility of implementing a quantum channel by local operations and classical communication (LOCC), even with an infinite number of rounds, and find that this can often be demonstrated by solving a set of linear equations. The method also allows one to design a LOCC protocol to implement the channel whenever such a protocol exists in any finite number of rounds. Perhaps surprisingly, the computational expense for analyzing LOCC channels is not much greater than that for LOCC measurements. We apply the method to several examples, two of which provide numerical evidence that the set of quantum channels that are not LOCC is not closed and that there exist channels that can be implemented by LOCC either in one round or in three rounds that are on the boundary of the set of all LOCC channels. Although every LOCC protocol must implement a separable quantum channel, it is a very difficult task to determine whether or not a given channel is separable. Fortunately, prior knowledge that the channel is separable is not required for application of our method.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
The generic quantum superintegrable system on the sphere and Racah operators
Iliev, Plamen
2017-06-01
We consider the generic quantum superintegrable system on the d-sphere with potential V(y)=\\sum _{k=1}^{d+1}b_k/y_k^2 , where b_k are parameters. Appropriately normalized, the symmetry operators for the Hamiltonian define a representation of the Kohno-Drinfeld Lie algebra on the space of polynomials orthogonal with respect to the Dirichlet distribution. The Gaudin subalgebras generated by Jucys-Murphy elements are diagonalized by families of Jacobi polynomials in d variables on the simplex. We define a set of generators for the symmetry algebra, and we prove that their action on the Jacobi polynomials is represented by the multivariable Racah operators introduced in Geronimo and Iliev (Constr Approx 31(3):417-457, 2010). The constructions also yield a new Lie-theoretic interpretation of the bispectral property for Tratnik's multivariable Racah polynomials.
All-high-Tc superconductor rapid-single-flux-quantum circuit operating at ˜30 K
Shokhor, S.; Nadgorny, B.; Gurvitch, M.; Semenov, V.; Polyakov, Yu.; Likharev, K.; Hou, S. Y.; Phillips, Julia M.
1995-11-01
We have implemented a simple circuit of the rapid single-flux-quantum (RSFQ) logic family using a single-layer YBa2Cu3O7-x thin-film structure with 14 in-plane Josephson junctions formed by direct electron beam writing. The circuit includes two dc/SFQ converters, two Josephson transmission lines, a complete RS SFQ flip-flop, and an SFQ/dc converter (readout SQUID). Low-frequency testing has shown that the dc-current-biased circuit operates correctly and reliably at T˜30 K, a few degrees below the effective critical temperature of the junctions. Prospects for a further increase of the operation temperature and implementation of more complex RSFQ circuits are discussed in brief.
A finite-dimensional representation of the quantum angular momentum operator
Campos, R G; Campos, Rafael G.
2000-01-01
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into polynomial subspaces of finite dimension and it can be interpreted as a generator of discrete rotations associated to the z-component of the projection of the angular momentum operator in such subspaces, inheriting thus some properties of the continuum operator. The group associated to these discrete rotations is the cyclic group of order N. Since the square of the quantum angular momentum L^2 is associated to a partial differential boundary value problem in the angular variables $\\theta$ and $\\phi$ whose solution is given in terms of the spherical harmonics, we can project such a differential equation to obtain an eigenvalue matrix problem of finite dimension by extending to several variables a projection technique for solving numerically two point boundary value problems and usi...
Energy Technology Data Exchange (ETDEWEB)
Niccoli, G.
2009-12-15
In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)
A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators.
Ochoa, Maicol A; Galperin, Michael; Ratner, Mark A
2014-11-12
We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.
40-GHz operation of a single-flux-quantum (SFQ) 4 × 4 switch scheduler
Kameda, Y.; Yorozu, S.; Hashimoto, Y.; Terai, H.; Fujimaki, A.; Yoshikawa, N.
2006-10-01
We designed a single-flux-quantum (SFQ) scheduler for a 4 × 4 network switch. It receives requests serially and arbitrates them. Fair scheduling is achieved by using a round-robin priority pointer at each output port. The pointer is updated so that the input port that was granted permission has the lowest priority in the next scheduling cycle. We divided the scheduler into sub-blocks, which were separately designed. The sub-blocks, which have asynchronous interfaces, were then connected with passive transmission lines. Ladder-type on-chip clock generators were included in the circuit for high-speed operation. Using logic simulation, we verified the scheduler test circuit. The scheduler test circuit was composed of about 3000 Josephson junctions. We tested the scheduler circuit at high speed and confirmed correct operations at over 40 GHz.
Distinct Lasing Operation From Chirped InAs/InP Quantum-Dash Laser
Khan, Mohammed Zahed Mustafa
2013-08-01
We study the enhanced inhomogeneity across the InAs quantum-dash (Qdash) layers by incorporating a chirped AlGaInAs barrier thickness in the InAs/InP laser structure. The lasing operation is investigated via Fabry-Pérot ridge-waveguide laser characterization, which shows a peculiar behavior under quasi-continuous-wave (QCW) operation. Continuous energy transfer between different dash ensembles initiated quenching of lasing action among certain dash groups, causing a reduced intensity gap in the lasing spectra. We discuss these characteristics in terms of the quasi-zero-dimensional density of states (DOS) of dashes and the active region inhomogeneity. © 2009-2012 IEEE.
Zaari, Ryan R; Brown, Alex
2010-01-07
Frequency domain shaped binary laser pulses were optimized to perform 2 qubit quantum gate operations in (12)C(16)O. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or pi, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.
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.
Towards optimizing two-qubit operations in three-electron double quantum dots
Frees, Adam; Gamble, John King; Mehl, Sebastian; Friesen, Mark; Coppersmith, S. N.
The successful implementation of single-qubit gates in the quantum dot hybrid qubit motivates our interest in developing a high fidelity two-qubit gate protocol. Recently, extensive work has been done to characterize the theoretical limitations and advantages in performing two-qubit operations at an operation point located in the charge transition region. Additionally, there is evidence to support that single-qubit gate fidelities improve while operating in the so-called ``far-detuned'' region, away from the charge transition. Here we explore the possibility of performing two-qubit gates in this region, considering the challenges and the benefits that may present themselves while implementing such an operational paradigm. This work was supported in part by ARO (W911NF-12-0607) (W911NF-12-R-0012), NSF (PHY-1104660), ONR (N00014-15-1-0029). The authors gratefully acknowledge support from the Sandia National Laboratories Truman Fellowship Program, which is funded by the Laboratory Directed Research and Development (LDRD) Program. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.
Q-operators, Yangian invariance and the quantum inverse scattering method
Frassek, Rouven
2014-01-01
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author's original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the fun...
2004-06-01
laser fundamentals , semiconductors, quantum wells and finally ending with a discussion of generic QC lasers. With the a priori knowledge that...quantum cascade laser structure and operation. It begins, in Chapter 2, with a discussion of the atom, continus with laser fundamentals , semiconductors...Aerospace Engineering, Arizona State University. 102 15. Chow, W. W. and Koch, S. W. Semiconductor- Laser Fundamentals . New York: Springer-Verlag
Microwave-driven coherent operation of a semiconductor quantum dot charge qubit.
Kim, Dohun; Ward, D R; Simmons, C B; Gamble, John King; Blume-Kohout, Robin; Nielsen, Erik; Savage, D E; Lagally, M G; Friesen, Mark; Coppersmith, S N; Eriksson, M A
2015-03-01
An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the 'sweet spot'. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z-axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography and gate set tomography. Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.
Huang, Ai-Jun; Shi, Jia-Dong; Wang, Dong; Ye, Liu
2017-02-01
In this work, we investigate the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and nonunital channels. Herein, we choose Pauli operators σ _x and σ _z as a pair of observables of interest measuring on particle A, and the uncertainty can be predicted when particle A is entangled with quantum memory B. We explore the dynamics of the uncertainty for the measurement under local unitary (phase-damping) and nonunitary (amplitude-damping) channels, respectively. Remarkably, we derive the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under various realistic noisy environments; it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose σ _x and σ _y measurement. Besides, we find out that the entropic uncertainty will have an optimal value if one chooses σ _x and σ _z as the measurement incompatibility, comparing with others. Furthermore, in order to reduce the entropic uncertainty in noisy environment, we propose an effective strategy to steer the amount by means of implementing a filtering operation on the particle under the two types of channels, respectively. It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength. Thus, our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.
Bovino, Fabio Antonio; Messina, Angelo
2016-10-01
In a very simplistic way, the Command and Control functions can be summarized as the need to provide the decision makers with an exhaustive, real-time, situation picture and the capability to convey their decisions down to the operational forces. This two-ways data and information flow is vital to the execution of current operations and goes far beyond the border of military operations stretching to Police and disaster recovery as well. The availability of off-the shelf technology has enabled hostile elements to endanger the security of the communication networks by violating the traditional security protocols and devices and hacking sensitive databases. In this paper an innovative approach based to implementing Device Independent Quantum Key Distribution system is presented. The use of this technology would prevent security breaches due to a stolen crypto device placed in an end-to-end communication chain. The system, operating with attenuated laser, is practical and provides the increasing of the distance between the legitimate users.
Above room temperature continuous wave operation of a broad-area quantum-cascade laser
Semtsiv, M. P.; Masselink, W. T.
2016-11-01
We describe the design and implementation of a broad-area (w ≈ 30 μm) quantum-cascade laser operating in a continuous wave mode up to heat-sink temperatures beyond +100 °C. The room-temperature emission wavelength is 4.6 μm. The temperature gradient in the active region of such a wide laser stripe is essentially perpendicular to the epitaxial layers and the resulting steady-state active region temperature offset scales approximately with the square of the number of cascades. With only 10 cascades in the active region, the threshold electrical power density in the current quantum-cascade laser in the continuous-wave mode is as low as Vth × Ith = 3.8 V × 0.9 kA/cm2 = 3.4 kW/cm2 at room temperature for 2 mm-long two-side high-reflectivity coated laser stripe. A 4 mm-long one-side high-reflectivity coated laser stripe delivers in continuous-wave mode above 0.6 W at +20 °C and above 1.3 W at -27 °C (cooled with a single-stage Peltier element). A 2 mm-long two-side high-reflectivity coated laser stripe demonstrates continuous-wave lasing up to at least +102 °C (375 K). The thermal conductance, Gth, ranges between 235 W/K cm2 and 140 W/K cm2 for temperatures between -33 °C and +102 °C. This demonstration opens the route for continuous-wave power scaling of quantum-cascade lasers via broad-area laser ridges.
Energy Technology Data Exchange (ETDEWEB)
Moroder, Tobias
2009-07-31
In this thesis we address several different topics within the field of quantum information theory. These results can be classified to either enhance the applicability of certain conceptual ideas to be more suited for an actual experimental situation or to ease the analysis for further investigation of central problems. In detail, the present thesis contains the following achievements: We start our discussion with the question under which conditions a given set of expectation values is compatible with the first and second moments of the spin operators of a generic spin j state. We link this characterization of physical moments to the Bosesymmetric extension problem for a particular two qubit state that is completely determined by the given moments. Via this reformulation we can provide operational sub- and superset approximations in order to identify moments which are assured to be physical and others which are clearly incompatible with quantum mechanics. We show that this operational approximate solution becomes more accurate for increasing total spin numbers j and converges to the exact solution in the limiting case. Another part deals with the theoretical concept of entanglement witnesses. In particular, we concentrate how to improve the detection strength of a linear entanglement witness by nonlinear terms. We analyze two distinguished cases: Either we optimize the iteration method for a given target state or we try to improve the entanglement witness with respect to all entangled states equally. In the remaining parts we discuss different options in order to make already existing ideas more applicable for actual experiments, since most of the famous applications in quantum information theory have only been introduced on a very idealized level and hence are not directly valid for the real experiment. We investigate the theoretical concept of a squash model, that represents an elegant ''evaluation trick'' to directly apply for instance the
Directory of Open Access Journals (Sweden)
Karen de la Vega-Hernández
2016-01-01
Full Text Available It is usually accepted that most 2D-NMR experiments cannot be approached using classical models. Instructors argue that Product Operators (PO or density matrix formalisms are the only alternative to get insights into complex spin evolution for experiments involving Multiple-Quantum Coherence, such as the Heteronuclear Multiple-Quantum Correlation (HMQC technique. Nevertheless, in recent years, several contributions have been published to provide vectorial descriptions for the HMQC taking PO formalism as the starting point. In this work we provide a graphical representation of the HMQC experiment, taking the basic elements of Bloch’s vector model as building blocks. This description bears an intuitive and comfortable understanding of spin evolution during the pulse sequence, for those who are novice in 2D-NMR. Finally, this classical vectorial depiction is tested against the PO formalism and nonclassical vectors, conveying the didactic advantage of shedding light on a single phenomenon from different perspectives. This comparative approach could be useful to introduce PO and nonclassical vectors for advanced upper-division undergraduate and graduate education.
High Operating Temperature Midwave Quantum Dot Barrier Infrared Detector (QD-BIRD)
Ting, David Z.; Soibel, Alexander; Hill, Cory J.; Keo, Sam A.; Mumolo, Jason M.; Gunapala, Sarath D.
2012-01-01
The nBn or XBn barrier infrared detector has the advantage of reduced dark current resulting from suppressed Shockley-Read-Hall (SRH) recombination and surface leakage. High performance detectors and focal plane arrays (FPAs) based on InAsSb absorber lattice matched to GaSb substrate, with a matching AlAsSb unipolar electron barrier, have been demonstrated. The band gap of lattice-matched InAsSb yields a detector cutoff wavelength of approximately 4.2 ??m when operating at 150K. We report results on extending the cutoff wavelength of midwave barrier infrared detectors by incorporating self-assembled InSb quantum dots into the active area of the detector. Using this approach, we were able to extend the detector cutoff wavelength to 6 ?m, allowing the coverage of the full midwave infrared (MWIR) transmission window. The quantum dot barrier infrared detector (QD-BIRD) shows infrared response at temperatures up to 225 K.
High Operating Temperature Midwave Quantum Dot Barrier Infrared Detector (QD-BIRD)
Ting, David Z.; Soibel, Alexander; Hill, Cory J.; Keo, Sam A.; Mumolo, Jason M.; Gunapala, Sarath D.
2012-01-01
The nBn or XBn barrier infrared detector has the advantage of reduced dark current resulting from suppressed Shockley-Read-Hall (SRH) recombination and surface leakage. High performance detectors and focal plane arrays (FPAs) based on InAsSb absorber lattice matched to GaSb substrate, with a matching AlAsSb unipolar electron barrier, have been demonstrated. The band gap of lattice-matched InAsSb yields a detector cutoff wavelength of approximately 4.2 ??m when operating at 150K. We report results on extending the cutoff wavelength of midwave barrier infrared detectors by incorporating self-assembled InSb quantum dots into the active area of the detector. Using this approach, we were able to extend the detector cutoff wavelength to 6 ?m, allowing the coverage of the full midwave infrared (MWIR) transmission window. The quantum dot barrier infrared detector (QD-BIRD) shows infrared response at temperatures up to 225 K.
Greene, Samuel M; Batista, Victor S
2017-09-12
We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.
Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory
Energy Technology Data Exchange (ETDEWEB)
Klymenko, M. V. [Department of Chemistry, University of Liège, B4000 Liège (Belgium); Klein, M. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Levine, R. D. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Crump Institute for Molecular Imaging and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine and Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095 (United States); Remacle, F., E-mail: fremacle@ulg.ac.be [Department of Chemistry, University of Liège, B4000 Liège (Belgium); The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-14
A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.
Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory
Klymenko, M. V.; Klein, M.; Levine, R. D.; Remacle, F.
2016-07-01
A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.
Benítez Rodríguez, E.; Arévalo Aguilar, L. M.; Piceno Martínez, E.
2017-03-01
To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.
Quantum limited noise figure operation of high gain erbium doped fiber amplifiers
DEFF Research Database (Denmark)
Lumholt, Ole; Povlsen, Jørn Hedegaard; Schüsler, Kim;
1993-01-01
powers below -5 dBm, and an improvement of 2.0 dB with a simultaneous gain increase of 4.1 dB is measured relative to a gain-optimized fiber. The optimum isolator location is evaluated for different pump and signal wavelengths in both an Al/Er-doped and a Ge/Er-doped fiber, for pump and signal power......Performance improvements obtained by using an isolator as an amplified-spontaneous-emission-suppressing component within erbium-doped fibers are evaluated. Simultaneous high-gain and near-quantum-limited noise figures can be obtained by such a scheme. The noise figure improves for input signal...... variations and different pump configurations. In all cases the optimum isolator position lies within 10-37% of the total fiber length for small signal operation...
Das, Ashok; Kalauni, Pushpa
2016-06-01
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter σ (0 ≤σ ≤β ) . We point out new features which arise when σ ≠β/2 in that the Hilbert space develops a natural, modified inner product different from the standard Dirac inner product. We construct the Bogoliubov transformation which connects the doubled vacuum state at zero temperature to the thermal vacuum in this case. We obtain the thermal Green's function (propagator) for the real massive Klein-Gordon theory as an expectation value in this thermal vacuum (with a modified inner product). The factorization of the thermal Green's function follows from this analysis. We also discuss, in the main text as well as in two appendices, various other interesting features which arise in such a description.
How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms
D'Ariano, G M
2006-01-01
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper quant-ph/0506034. Pivotal roles are played by the "local observability principle", which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of "informationally complete observables" and of a "symmetric faithful state". This last notion allows one to introduce an operational definition for the real version of the "adjoint"--i. e. the transposition--from which one can derive a real Hilbert-space structure via either the Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in detail only the Gelfand-Naimark-Segal construction, which leads to a real Hilbert space structure analogous to that...
Velocity operator and velocity field for spinning particles in (non-relativistic) quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[INFN, Milan (Italy)]|[Campinas State Univ., SP (Brazil). Dept. of Applied Math.; Salesi, G. [Catania Univ. (Italy). Dip. di Fisica
1995-06-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, the paper introduces - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, a new (non-relativistic) velocity operator for a spin 1/2 particle is also proposed. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of- mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which the constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current.
Quantum theory with an energy operator defined as a quartic form of the momentum
Bezák, Viktor
2016-09-01
Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke-Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined by the Yurke-Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.
Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.
2017-09-01
The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.
Goudarzi, H.; Dousti, M. J.; Shafaei, A.; Pedram, M.
2014-05-01
This paper presents a physical mapping tool for quantum circuits, which generates the optimal universal logic block (ULB) that can, on average, perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling, whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (1) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (2) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (3) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different FT quantum operations mapped onto different ULB sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies. Experimental results show an average latency reduction of about 40 % compared to previous work.
Cibella, S.; Beck, M.; Carelli, P.; Castellano, M. G.; Chiarello, F.; Faist, J.; Leoni, R.; Ortolani, M.; Sabbatini, L.; Scalari, G.; Torrioli, G.; Turcinkova, D.
2012-06-01
We make use of a niobium film to produce a micrometric vacuum-bridge superconducting bolometer responding to THz frequency. The bolometer works anywhere in the temperature range 2-7 K, which can be easily reached in helium bath cryostats or closed-cycle cryocoolers. In this work the bolometer is mounted on a pulse tube refrigerator and operated to measure the equivalent noise power (NEP) and the response to fast (μs) terahertz pulses. The NEP above 100 Hz equals that measured in a liquid helium cryostat showing that potential drawbacks related to the use of a pulse tube refrigerator (like mechanical and thermal oscillations, electromagnetic interference, noise) are irrelevant. At low frequency, instead, the pulse tube expansion-compression cycles originate lines at 1 Hz and harmonics in the noise spectrum. The bolometer was illuminated with THz single pulses coming either from a Quantum Cascade Laser operating at liquid nitrogen temperature or from a frequency-multiplied electronic oscillator. The response of the bolometer to the single pulses show that the device can track signals with a rise time as fast as about 450 ns.
,
2011-01-01
Around the globe several observatories are seeking the first direct detection of gravitational waves (GWs). These waves are predicted by Einstein's General Theory of Relativity [Einstein, A., Annalen der Physik 49, 769-822 (1916)] and are generated e.g. by black-hole binary systems [Sathyaprakash, B. S. and Schutz, B. F., Living Rev. Relativity 12, 2 (2009)]. Current GW detectors are Michelson-type kilometer-scale laser interferometers measuring the distance changes between in vacuum suspended mirrors. The sensitivity of these detectors at frequencies above several hundred hertz is limited by the vacuum (zero-point) fluctuations of the electromagnetic field. A quantum technology - the injection of squeezed light [Caves, C. M., Phys. Rev. D 23, 1693-1708 (1981)] - offers a solution to this problem. Here we demonstrate the squeezed-light enhancement of GEO600, which will be the GW observatory operated by the LIGO Scientific Collaboration in its search for GWs for the next 3-4 years. GEO600 now operates with its...
Quantum-mechanical tunneling differential operators, zeta-functions and determinants
Casahorrán, J
2002-01-01
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral method. Once we perform the Wick rotation, the euclidean equation of motion is the same as the usual one for the point particle in real time, except that the potential at issue is turned upside down. In doing so, our double-well potential becomes a two-humped potential. As required by the semiclassical approximation we may study the quadratic fluctuations over the instanton which represents in this context the localised finite-action solutions of the euclidean equation of motion. The determinants of the quadratic differential operators are evaluated by means of the zeta-function method. We write in closed form the eigenfunctions as well as the energy eigenvalues corresponding to such operators by using the shape-invariance symmetry. The effect of the multi-instantons configu...
Quantum cascade lasers operating from 1.4 to 4 THz
Institute of Scientific and Technical Information of China (English)
Sushil Kumar
2011-01-01
The development of teranertz (THz) quantum cascade lasers (QCLs) has progressed considerably since their advent almost a decade ago. THz QCLs operating in a frequency range from 1.4 to 4 THz with electron-phonon scattering mediated depopulation schemes are described. Several different types of GaAs/AlGaAs superlattice designs are reviewed. Some of the best temperature performances are obtained by the so-called resonant-phonon designs that are described. Operation above a temperature of 160 K has been obtained across the spectrum for THz QCLs operating at v > 1.8 THz. The maximum operating temperature of previously reported THz QCLs has empirically been limited to a value of ~ hω/kB- A new design scheme for THz QCLs with scattering-assisted injection is shown to surpass this empirical temperature barrier, and is promising to improve the maximum operating temperatures of THz QCLs even further.%1.IntroductionHigh-power sources of terahertz (THz) radiation are required for a multitude of applications in sensing,imaging,and spectroscopy in fields as diverse as astronomy,medicine,security,pharmaceuticals and so-forth.THz science and technology has advanced significantly in the recent years[1,2] especially toward the realization of novel THz radiation sources.In comparison to narrow-band sources such as lasers,broadband sources of terahertz radiation are more widely available;however,such sources are inherently low power (average power is of the order of few micro-Watts).They are useful nevertheless because of room temperature operation and for their ability to be detected coherently.Techniques such as generation of THz bandwidth time-domain pulses in high resistivity semiconductors[3],non-linear generation by electrooptical-rectification in crystals such as ZnTe[4],or nonlinear generation by optical parametric conversion in materials such as LiNbO3[5] or by difference-frequency generation in semiconductors[6],have been used for various raster-scanned imaging and
High-power, surface-emitting quantum cascade laser operating in a symmetric grating mode
Energy Technology Data Exchange (ETDEWEB)
Boyle, C.; Sigler, C.; Kirch, J. D.; Botez, D.; Mawst, L. J., E-mail: mawst@engr.wisc.edu [Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Lindberg, D. F.; Earles, T. [Intraband, LLC, Madison, Wisconsin 53726 (United States)
2016-03-21
Grating-coupled surface-emitting (GCSE) lasers generally operate with a double-lobed far-field beam pattern along the cavity-length direction, which is a result of lasing being favored in the antisymmetric grating mode. We experimentally demonstrate a GCSE quantum-cascade laser design allowing high-power, nearly single-lobed surface emission parallel to the longitudinal cavity. A 2nd-order Au-semiconductor distributed-feedback (DFB)/distributed-Bragg-reflector (DBR) grating is used for feedback and out-coupling. The DFB and DBR grating regions are 2.55 mm- and 1.28 mm-long, respectively, for a total grating length of 5.1 mm. The lasers are designed to operate in a symmetric (longitudinal) grating mode by causing resonant coupling of the guided optical mode to the antisymmetric surface-plasmon modes of the 2nd-order metal/semiconductor grating. Then, the antisymmetric modes are strongly absorbed by the metal in the grating, causing the symmetric mode to be favored to lase, which, in turn, produces a single-lobed beam over a range of grating duty-cycle values of 36%–41%. Simulations indicate that the symmetric mode is always favored to lase, independent of the random phase of reflections from the device's cleaved ends. Peak pulsed output powers of ∼0.4 W were measured with nearly single-lobe beam-pattern (in the longitudinal direction), single-spatial-mode operation near 4.75 μm wavelength. Far-field measurements confirm a diffraction-limited beam pattern, in agreement with simulations, for a source-to-detector separation of 2 m.
Ermilov, A. S.; Zobov, V. E.
2007-12-01
To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.
2003-01-01
Japanese Journal of Applied Physics , 40, part 1, (no. 3B), 1857-1895 2001 P. P. Paskov, P. O. Holtz, B. Monemar, J. M...Garcia, W. V. Schoenfeld, P. M. Petroff “Excited state magnetoluminescence of InAs/GaAs self-assembled quantum dots” Japanese Journal of Applied Physics , 40...heterostructures grown by plasma-assisted molecular beam epitaxy” Japanese Journal of Applied Physics , 40, part 1, (no. 11),
On the Relationship between the Moyal Algebra and the Quantum Operator Algebra of von Neumann
Hiley, B. J.
2012-01-01
The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of the characteristic function which immediately provides a probability distribution. The approach is sometimes perceived negatively merely as an attempt to return to classical notions, but the mathematics Moyal develops is simply a re-expression of what is a...
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Institute of Scientific and Technical Information of China (English)
ZHOU Nan-run; GONG Li-hua; LIU Ye
2006-01-01
In this letter a cascade quantum teleportation scheme is proposed. The proposed scheme needs less local quantum operations than those of quantum multi-teleportation. A quantum teleportation scheme based on entanglement swapping is presented and compared with the cascade quantum teleportation scheme. Those two schemes can effectively teleport quantum information and extend the distance of quantum communication.
Ma, Shao-Qiang; Zhu, Han-Jie; Zhang, Guo-Feng
2017-04-01
The effects of different quantum feedback types on the estimation precision of the detection efficiency are studied. It is found that the precision can be more effective enhanced by a certain feedback type through comparing these feedbacks and the precision has a positive relation with detection efficiency for the optimal feedback when the system reach the state of dynamic balance. In addition, the bigger the proportion of |1> is the higher the precision is and we will not obtain any information about the parameter to be estimated if |0> is chosen as initial state for the feedback type λσz.
The Heteronuclear Single-Quantum Correlation (HSQC) Experiment: Vectors versus Product Operators
de la Vega-Herna´ndez, Karen; Antuch, Manuel
2015-01-01
A vectorial representation of the full sequence of events occurring during the 2D-NMR heteronuclear single-quantum correlation (HSQC) experiment is presented. The proposed vectorial representation conveys an understanding of the magnetization evolution during the HSQC pulse sequence for those who have little or no quantum mechanical background.…
2017-03-06
in nitrogen-vacancy diamond, high-dimensional quantum key distribution, and photonic integrated circuits for quantum communication and computation ...Raytheon BBN Technologies; Dr. Saikat Guha Contractor Address: 10 Moulton Street, Cambridge, MA 02138 Title of the Project: COmmunications and...Contract Data Requirements List In accordance with the reference requirement of the subject contract, Raytheon BBN Technologies (BBN) hereby submits
Dynamic Quantum Allocation and Swap-Time Variability in Time-Sharing Operating Systems.
Bhat, U. Narayan; Nance, Richard E.
The effects of dynamic quantum allocation and swap-time variability on central processing unit (CPU) behavior are investigated using a model that allows both quantum length and swap-time to be state-dependent random variables. Effective CPU utilization is defined to be the proportion of a CPU busy period that is devoted to program processing, i.e.…
The Quantum-Like Brain Operating on Subcognitive and Cognitive Time Scales
Khrennikov, Andrei
2007-01-01
We propose a {\\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\\it quantum} model. By the latter cognition is created by {\\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a very general formalism describing {\\it consistent processing of incomplete information} about contexts (physical, mental, economic, social). The brain is an advanced device which developed the ability to create a QL representation of contexts. Therefore its functioning can also be described by the mathematical formalism of QM. The possibility of such a description has nothing to do with composing of the brain of quantum systems (photons, electrons, protons,...). Moreover, we shall propose a model in that the QL representation is based on conventional neurophysiological model of the functioning of the brain. The brain uses the QL rule (given ...
Operation of a superconducting nanowire quantum interference device with mesoscopic leads
Pekker, David; Bezryadin, Alexey; Hopkins, David S.; Goldbart, Paul M.
2005-09-01
A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultranarrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions—length or width—lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A detailed theory, encompassing this phenomenology quantitatively, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil’berman-Ambegaokar-Halperin theory of intrinsic resistive fluctuations in a current-biased Josephson junction and the Langer-Ambegaokar-McCumber-Halperin theory of intrinsic resistive fluctuations in a superconducting wire. In particular, it is demonstrated that via the resistance of the NQUID, the wires act as a probe of spatial variations in the superconducting order parameter along the perimeter of each lead: in essence, a superconducting phase gradiometer.
Cheon, T
2004-01-01
We show that the U(2) family of point interactions on a line can be utilized to provide the U(2) family of qubit operations for quantum information processing. Qubits are realized as localized states in either side of the point interaction which represents a controllable gate. The manipulation of qubits proceeds in a manner analogous to the operation of an abacus. Keywords: quantum computation, quantum contact interaction, quantum wire
Measurement-induced operation of two-ion quantum heat machines
Chand, Suman; Biswas, Asoka
2017-03-01
We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.
Lanzagorta, Marco
2011-01-01
This book offers a concise review of quantum radar theory. Our approach is pedagogical, making emphasis on the physics behind the operation of a hypothetical quantum radar. We concentrate our discussion on the two major models proposed to date: interferometric quantum radar and quantum illumination. In addition, this book offers some new results, including an analytical study of quantum interferometry in the X-band radar region with a variety of atmospheric conditions, a derivation of a quantum radar equation, and a discussion of quantum radar jamming.This book assumes the reader is familiar w
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Energy Technology Data Exchange (ETDEWEB)
Kalay, Berfin; Demiralp, Metin [İstanbul Technical University, Informatics Institute, Maslak, 34469, İstanbul (Turkey)
2015-12-31
This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.
Carrasco-Casado, Alberto; Fernandez, Veronica
2014-01-01
Free-space quantum key distribution links in urban environment have demanding operating needs, such as functioning in daylight and under atmospheric turbulence, which can dramatically impact their performance. Both effects are usually mitigated with a careful design of the field of view of the receiver. However, a trade-off is often required, since a narrow field of view improves background noise rejection but it is linked to an increase in turbulence-related losses. In this paper, we present a high-speed automatic tracking system to overcome these limitations. Both a reduction in the field-of-view to decrease the background noise and the mitigation of the losses caused by atmospheric turbulence are addressed. Two different designs are presented and discussed, along with technical considerations for the experimental implementation. Finally, preliminary experimental results of beam wander correction are used to estimate the potential improvement of both the quantum bit error rate and secret key rate of a free ...
Energy Technology Data Exchange (ETDEWEB)
Baykara, N. A. [Marmara University, Faculty of Sciences and Letters, Mathematics Department, Göztepe Campus, 34730, Istanbul (Turkey)
2015-12-31
Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.
On the operation of machines powered by quantum non-thermal baths
Niedenzu, Wolfgang; Gelbwaser-Klimovsky, David; Kofman, Abraham G.; Kurizki, Gershon
2016-08-01
Diverse models of engines energised by quantum-coherent, hence non-thermal, baths allow the engine efficiency to transgress the standard thermodynamic Carnot bound. These transgressions call for an elucidation of the underlying mechanisms. Here we show that non-thermal baths may impart not only heat, but also mechanical work to a machine. The Carnot bound is inapplicable to such a hybrid machine. Intriguingly, it may exhibit dual action, concurrently as engine and refrigerator, with up to 100% efficiency. We conclude that even though a machine powered by a quantum bath may exhibit an unconventional performance, it still abides by the traditional principles of thermodynamics.
Fujita, Kazuue; Ito, Akio; Hitaka, Masahiro; Dougakiuchi, Tatsuo; Edamura, Tadataka
2017-08-01
The performance of a room-temperature continuous-wave (CW) terahertz source based on intracavity difference-frequency generation in a mid-infrared (λ ∼ 6.8 µm) quantum cascade laser with a dual-upper-state active region is reported. The fabricated buried heterostructure device, with a two-section buried distributed feedback grating, operates at two mid-infrared wavelengths and demonstrates a terahertz output of 2.92 THz with a very low threshold current density of 0.89 kA/cm2 in pulsed operation. Consequently, despite an epitaxial-side-up mounting configuration, the device achieves CW operation at room temperature in which a low CW threshold current density of 1.3 kA/cm2 is obtained.
Zaari, Ryan R; Brown, Alex
2011-07-28
The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Cheng, Liwei
Quantum cascade lasers (QCLs) that emit in the mid-infrared (IR) range between 3 and 10 µm of the electromagnetic spectrum play an important role in optical gas sensing and molecular spectroscopic applications because several important environmental molecules such as CO, CO2, CH 4, and NH3 are known to exhibit strong absorption lines in this mid-IR range. To differentiate such fine absorption features as narrow as a few angstroms, a single-mode QCL with an extremely narrow spectral linewidth, broadly tunable over the molecular absorption fingerprints and operating at sufficient optical power at room temperature, is highly desirable. We present, in this dissertation, two major studies on mid-IR QCLs, one being an improvement in device performance through a buried-heterostructure (BH) regrowth study, and the other being a realization of single-mode, tunable QCLs integrated with a distributed-Bragg-reflector (DBR) grating and thermal tuning mechanism. Efficient heat dissipation in the QCL active region, which is crucial for high optical-power operation, can be effectively achieved using BH waveguides laterally embedded with InP grown by metal-organic chemical vapor disposition (MOCVD). We have experimentally examined the effects of the structural features of mesas, such as the mesa orientation, geometry, sidewall-etched profile, and the length of oxide overhang, on the BH regrowth. We find that the mesa oriented in the [011¯] direction with smoothly etched sidewalls produces a satisfactory planar growth profile and uniform lateral growth coverage and that a mesa-height-to-overhang-length ratio between 2.5 and 3.0 is effective in reducing anomalous growth in the vicinity of oxide edges. As a result, high-power QCLs capable of producing multi-hundred milliwatts at room temperature at ˜4.6 µm and ˜7.9 µm through reproducible BH regrowth results have been demonstrated. We have also demonstrated single-mode tunable QCLs operating at ˜7.9 µm with an internal DBR
Injection locking of quantum dot microlasers operating in the few photon regime
Schlottmann, Elisabeth; Lingnau, Benjamin; Lüdge, Kathy; Schneider, Christian; Kamp, Martin; Höfling, Sven; Wolters, Janik; Reitzenstein, Stephan
2016-01-01
We experimentally and theoretically investigate injection locking of quantum dot (QD) microlasers in the regime of cavity quantum electrodynamics (cQED). We observe frequency locking and phase-locking where cavity enhanced spontaneous emission enables simultaneous stable oscillation at the master frequency and at the solitary frequency of the slave microlaser. Measurements of the second-order autocorrelation function prove this simultaneous presence of both master and slave-like emission, where the former has coherent character with $g^{(2)}(0)=1$ while the latter one has thermal character with $g^{(2)}(0)=2$. Semi-classical rate-equations explain this peculiar behavior by cavity enhanced spontaneous emission and a low number of photons in the laser mode.
On the class of possible nonlocal anyon-like operators and quantum groups
Chaichian, Masud; Montonen, Claus
1993-01-01
We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.
Quantum Diaries Blog: Is the moon full? Just ask the LHC operators
Pauline Gagnon
2012-01-01
Corrections to proton orbits in the LHC appear as regular dips in the instantaneous luminosity measured by CMS (beige) and ATLAS (green). The LHC is so large that the gravitational force exerted by the moon is not the same at all points, which creates small distortions of the tunnel. And the machine is sensitive enough to detect minute deformations created by the small differences in gravitational force across its diameter. Therefore, the orbits of protons in the accelerator have to be adjusted regularly to account for the gravitational effect of the moon. Read more on the Quantum Diaries Blog post.
RT CW operation of InGaN multi-quantum-well structure laser diodes
Shuji Nakamura
1998-01-01
Gallium nitride and other III–Vnitride-based semiconductors have a direct band gap that is suitable for blue light-emitting devices. The band gap energy of aluminium gallium indium nitride (AIInGaN) varies between 6.2 and 2.0 eV, depending on its composition at room temperature. Thus, using these semiconductors, red to UV emitting devices are fabricated. High efficient UV, blue and green InGaN single-quantum-well (SQW) structure light-emitting diodes (LEDs) have been fabricated with the exter...
A Quantum Computational Semantics for Epistemic Logical Operators. Part II: Semantics
Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe
2014-10-01
By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that π is irrational". One is dealing with a holistic form of quantum computational semantics, where entanglement plays a fundamental role; thus, the meaning of a global expression determines the contextual meanings of its parts, but generally not the other way around. The epistemic situations represented in this semantics seem to reflect some characteristic limitations of the real processes of acquiring information. Since knowledge is not generally closed under logical consequence, the unpleasant phenomenon of logical omniscience is here avoided.
Adiabatic phase-conserving processes for executing quantum operations with ultracold atoms
Beterov, I. I.; Tret'yakov, D. B.; Entin, V. M.; Yakshina, E. A.; Khamzina, G. N.; Ryabtsev, I. I.
2017-06-01
We have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
Quantum singular operator limits of thin Dirichlet tubes via $\\Gamma$-convergence
de Oliveira, Cesar R.
2010-01-01
The $\\Gamma$-convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure to obtain the effective Schr\\"odinger operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
Weaver, Nik
2010-01-01
We define a "quantum relation" on a von Neumann algebra M \\subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively representation independent. Quantum relations on l^\\infty(X) exactly correspond to subsets of X^2, i.e., relations on X. There is also a good definition of a "measurable relation" on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, we can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and we can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. We are also able to intrinsically characterize the quantum relations on M in terms of families of projections in M \\otimes B(l^2).
Razavipour, S. G.; Dupont, E.; Fathololoumi, S.; Chan, C. W. I.; Lindskog, M.; Wasilewski, Z. R.; Aers, G.; Laframboise, S. R.; Wacker, A.; Hu, Q.; Ban, D.; Liu, H. C.
2013-05-01
We designed and demonstrated a terahertz quantum cascade laser based on indirect pump injection to the upper lasing state and phonon scattering extraction from the lower lasing state. By employing a rate equation formalism and a genetic algorithm, an optimized active region design with four-well GaAs/Al0.25Ga0.75As cascade module was obtained and epitaxially grown. A figure of merit which is defined as the ratio of modal gain versus injection current was maximized at 150 K. A fabricated device with a Au metal-metal waveguide and a top n+ GaAs contact layer lased at 2.4 THz up to 128.5 K, while another one without the top n+ GaAs lased up to 152.5 K (1.3ℏω /kB). The experimental results have been analyzed with rate equation and nonequilibrium Green's function models. A high population inversion is achieved at high temperature using a small oscillator strength of 0.28, while its combination with the low injection coupling strength of 0.85 meV results in a low current. The carefully engineered wavefunctions enhance the quantum efficiency of the device and therefore improve the output optical power even with an unusually low injection coupling strength.
Continuous operation of four-state continuous-variable quantum key distribution system
Matsubara, Takuto; Ono, Motoharu; Oguri, Yusuke; Ichikawa, Tsubasa; Hirano, Takuya; Kasai, Kenta; Matsumoto, Ryutaroh; Tsurumaru, Toyohiro
2016-10-01
We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|+/-α⟩,|+/-𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.
RT CW operation of InGaN multi-quantum-well structure laser diodes
Directory of Open Access Journals (Sweden)
Shuji Nakamura
1998-01-01
Full Text Available Gallium nitride and other III–Vnitride-based semiconductors have a direct band gap that is suitable for blue light-emitting devices. The band gap energy of aluminium gallium indium nitride (AIInGaN varies between 6.2 and 2.0 eV, depending on its composition at room temperature. Thus, using these semiconductors, red to UV emitting devices are fabricated. High efficient UV, blue and green InGaN single-quantum-well (SQW structure light-emitting diodes (LEDs have been fabricated with the external quantum efficiencies of 7.5% at 371 nm (UV, 11.2% at 468 nm (blue and 11.6% at 520 nm (green, respectively, which were the highest values ever reported for the LEDs with those shorter emission wavelengths. The luminous efficiencies of blue and green LEDs were 5 lm/W and 30 lm/W, respectively, which values are almost identical to that of the white conventional incandescent bulb lamp (20 lm/W. By combining the blue, green and red LEDs, we could fabricate white LEDs with a luminous efficiency of 20–30 im/W which is almost comparable to that of the incandescent bulb lamp. Thus, we can replace the conventional incandescent bulb lamps with these LEDs in order to save an energy consumption and natural resources now.
Parniak, Michał; Wasilewski, Wojciech
2015-01-01
We analyze the properties of a Raman quantum light-atom interface in long atomic ensemble and its applications as a quantum memory or two-mode squeezed state generator. We include both Stokes and anti-Stokes scattering and the effects of Doppler broadening in buffer gas assuming frequent velocity-averaging collisions. We find the Green functions describing multimode transformation from input to output fields of photons and atomic excitations. Proper mode basis is found via singular value decomposition. It reveals that triples of modes are coupled by a transformation equivalent to a combination of two beamsplitters and a two-mode squeezing operation. We analyze the possible transformations on an example of warm rubidium-87 vapor. We find that the fidelity of the mapping of a single excitation between the memory and light is strictly limited by the fractional contribution of the Stokes scattering in predominantly anti-Stokes process. The model we present bridges the gap between the Stokes only and anti-Stokes o...
Efficiency at maximum power output of quantum heat engines under finite-time operation
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1-Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2-ηC) and from below by ηC/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ηCA=1-Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Experimental evidence of hot carriers solar cell operation in multi-quantum wells heterostructures
Energy Technology Data Exchange (ETDEWEB)
Rodière, Jean; Lombez, Laurent, E-mail: laurent.lombez@chimie-paristech.fr [IRDEP, Institute of R and D on Photovoltaic Energy, UMR 7174, CNRS-EDF-Chimie ParisTech, 6 Quai Watier-BP 49, 78401 Chatou Cedex (France); Le Corre, Alain; Durand, Olivier [INSA, FOTON-OHM, UMR 6082, F-35708 Rennes (France); Guillemoles, Jean-François [IRDEP, Institute of R and D on Photovoltaic Energy, UMR 7174, CNRS-EDF-Chimie ParisTech, 6 Quai Watier-BP 49, 78401 Chatou Cedex (France); NextPV, LIA CNRS-RCAST/U. Tokyo-U. Bordeaux, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904 (Japan)
2015-05-04
We investigated a semiconductor heterostructure based on InGaAsP multi quantum wells (QWs) using optical characterizations and demonstrate its potential to work as a hot carrier cell absorber. By analyzing photoluminescence spectra, the quasi Fermi level splitting Δμ and the carrier temperature are quantitatively measured as a function of the excitation power. Moreover, both thermodynamics values are measured at the QWs and the barrier emission energy. High values of Δμ are found for both transition, and high carrier temperature values in the QWs. Remarkably, the quasi Fermi level splitting measured at the barrier energy exceeds the absorption threshold of the QWs. This indicates a working condition beyond the classical Shockley-Queisser limit.
Quantum logic operations on two distant atoms trapped in two optical-fibre-connected cavities
Institute of Scientific and Technical Information of China (English)
Zhang Ying-Qiao; Zhang Shou; Yeon Kyu-Hwang; Yu Seong-Cho
2011-01-01
Based on the coupling of two distant three-level atoms in two separate optical cavities connected with two optical fibres,schemes on the generation of several two-qubit logic gates are discussed under the conditions of △ =δ -2v cos πk/2 (》) g/2 and (v～ g).Discussion and analysis of the fidelity,gate time and experimental setups show that our schemes are feasible with current optical cavity,atomic trap and optical fibre techniques.Moreover,the atom-cavityfibre coupling can be used to generate an N-qubit nonlocal entanglement and transfer quantum information among N distant atoms by arranging N atom-cavity assemblages in a line and connecting each two adjacent cavities with two optical fibres.
Efficiency at maximum power output of quantum heat engines under finite-time operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Influence of vertical coupling on the lasing operation of quantum-dash laser
Khan, Mohammed Zahed Mustafa
2012-01-01
The authors numerically investigated the consequence of vertical coupling among multi-stack InAs quantum dash (Qdash) laser structure on the lasing bandwidth. The developed model is based on multi-population carrier-photon rate equation and incorporates inhomogeneous broadening due to dash size or composition fluctuation, homogeneous broadening of optical gain, and the multi-longitudinal photon modes. In addition, the effect of Qdash layers emitting at different wavelength, and the carrier coupling (tunneling) between adjacent stacks, are also accounted for. The results predict a direct relation between the lasing bandwidth and the barrier thickness and hence enhanced lasing bandwidth could be achieved by decoupling the Qdash layers (large barrier thickness). Moreover, the model further affirms the non-equilibrium distribution of carriers among Qdash layers in a multi-stack laser structure.
Sokolova, Z. N.; Pikhtin, N. A.; Tarasov, I. S.; Asryan, L. V.
2016-08-01
A model for calculating the operating characteristics of semiconductor quantum well (QW) lasers is presented. The model exploits the condition of global electroneutrality, which includes the charge carriers both in the two-dimensional (2D) active region (QW) and bulk waveguide region (optical confinement layer - OCL). The charge of each sign in the OCL is shown to be significantly larger than that in the QW. As a result of this, (i) the global electroneutrality condition reduces to the condition of electroneutrality in the OCL and (ii) the local electroneutrality in the QW can be strongly violated, i.e., the 2D electron and hole densities in the QW can significantly differ from each other.
Xie, Feng; Caneau, Catherine; LeBlanc, Herve P.; Coleman, Sean; Hughes, Lawrence C.; Zah, Chung-en
2012-03-01
We demonstrated the room temperature continuous wave (CW) operation of mid-infrared distributed feedback (DFB) quantum cascade lasers (QCLs) made of strain balanced GaInAs/AlInAs material on InP substrates for sensing CO2 isotope and N2O gas for potential applications that need battery powered portable devices in a sensor network. For the former device at 4.35 μm wavelength, we demonstrated a low threshold voltage of less than 8 V for battery operation and a near circular far field pattern with small divergent angles of 33 by 28 degrees full width at half maximum (FWHM) in vertical and horizontal directions, respectively, for easy collimation. For the latter device at 4.5 μm wavelength, we demonstrated a low CW threshold power consumption of 0.7 W at 20 °C. A side mode suppression ratio (SMSR) of 30 dB was achieved within the whole operating current and temperature ranges for both lasers.
Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
Gukov, Sergei
2013-01-01
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.
量子算符的次序%Quantum operator ordering
Institute of Scientific and Technical Information of China (English)
张寿; 李哲奎
2000-01-01
考虑了由正则变换相关的谐振子Hamiltonian.并且利用Feyman路径积分,讨论了算符次序问题.%The harmonic Hamiltonian system related by canonical transformation are considered. And using Feynman path integral we discussed the operator ordering problem.
Quantum Logic Operation with Single Trapped Ion Without Limitation of Lamb-Dicke Parameter
Institute of Scientific and Technical Information of China (English)
ZHANG Rong; ZHU Shi-Qun
2003-01-01
By applying the nonlinear interaction between internal and external degrees of a trapped ion with theassistance of two pairs or three pairs of laser beams that are perpendicular to each other, the realization of quantumlogic operation without the limitation on the Lamb-Dicke parameter can be achieved when the lasers are tuned to thecarrier.
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....
Low-noise nano superconducting quantum interference device operating in Tesla magnetic fields.
Schwarz, Tobias; Nagel, Joachim; Wölbing, Roman; Kemmler, Matthias; Kleiner, Reinhold; Koelle, Dieter
2013-01-22
Superconductivity in the cuprate YBa(2)Cu(3)O(7) (YBCO) persists up to huge magnetic fields (B) up to several tens of Teslas, and sensitive direct current (dc) superconducting quantum interference devices (SQUIDs) can be realized in epitaxially grown YBCO films by using grain boundary Josephson junctions (GBJs). Here we present the realization of high-quality YBCO nanoSQUIDs, patterned by focused ion beam milling. We demonstrate low-noise performance of such a SQUID up to B = 1 T applied parallel to the plane of the SQUID loop at the temperature T = 4.2 K. The GBJs are shunted by a thin Au layer to provide nonhysteretic current voltage characteristics, and the SQUID incorporates a 90 nm wide constriction which is used for on-chip modulation of the magnetic flux through the SQUID loop. The white flux noise of the device increases only slightly from 1.3 μΦ(0)/(Hz)(1/2) at B = 0 to 2.3 μΦ(0)/(Hz))(1/2) at 1 T. Assuming that a point-like magnetic particle with magnetization in the plane of the SQUID loop is placed directly on top of the constriction and taking into account the geometry of the SQUID, we calculate a spin sensitivity S(μ)(1/2) = 62 μ(B)/(Hz))(1/2) at B = 0 and 110 μ(B)/(Hz))(1/2) at 1 T. The demonstration of low noise of such a SQUID in Tesla fields is a decisive step toward utilizing the full potential of ultrasensitive nanoSQUIDs for direct measurements of magnetic hysteresis curves of magnetic nanoparticles and molecular magnets.
A note on the correspondence between qubit quantum operations and special relativity
Energy Technology Data Exchange (ETDEWEB)
Arrighi, Pablo [Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge CB3 0FD (United Kingdom); Patricot, Christophe [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2003-05-23
We exploit a well-known isomorphism between complex Hermitian 2 x 2 matrices and R{sup 4}, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in E{sup 1,3}, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences. (letter to the editor)
A Note on the correspondence between Qubit Quantum Operations and Special Relativity
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2003-01-01
We exploit a well-known isomorphism between complex hermitian $2\\times 2$ matrices and $\\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map into a Minkowskian cone in $\\mathbb{E}^{(3,1)}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with an informal discussion of the equivalence and some of its possible consequences.
Quantum corrections to the effective neutrino mass operator in 5D MSSM
Energy Technology Data Exchange (ETDEWEB)
Deandrea, Aldo; Welzel, Julien [Universite de Lyon 1, Institut de Physique Nucleaire, 4 rue E. Fermi, 69622 Villeurbanne Cedex (France); Hosteins, Pierre [SPhT, CEA-Saclay, 91191 Gif-sur-Yvette cedex (France); Oertel, Micaela [LUTH, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon (France)
2007-04-15
We discuss in detail a five-dimensional Minimal Supersymmetric Standard Model compactified on S{sup 1}/Z{sub 2} extended by the effective Majorana neutrino mass operator. We study the evolution of neutrino masses and mixings. Masses and angles, in particular the atmospheric mixing angle {theta}{sub 23}, can be significantly lowered at high energies with respect to their value at low energy. (authors)
Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?
Berenstein, David; Miller, Alexandra
2017-06-30
In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.
Singh, Manu Pratap; Rajput, B. S.
2016-03-01
Recall operations of quantum associative memory (QuAM) have been conducted separately through evolutionary as well as non-evolutionary processes in terms of unitary and non- unitary operators respectively by separately choosing our recently derived maximally entangled states (Singh-Rajput MES) and Bell's MES as memory states for various queries and it has been shown that in each case the choices of Singh-Rajput MES as valid memory states are much more suitable than those of Bell's MES. it has been demonstrated that in both the types of recall processes the first and the fourth states of Singh-Rajput MES are most suitable choices as memory states for the queries `11' and `00' respectively while none of the Bell's MES is a suitable choice as valid memory state in these recall processes. It has been demonstrated that all the four states of Singh-Rajput MES are suitable choice as valid memory states for the queries `1?', `?1', `?0' and `0?' while none of the Bell's MES is suitable choice as the valid memory state for these queries also.
Leang, Sarom S; Rendell, Alistair P; Gordon, Mark S
2014-03-11
Increasingly, modern computer systems comprise a multicore general-purpose processor augmented with a number of special purpose devices or accelerators connected via an external interface such as a PCI bus. The NVIDIA Kepler Graphical Processing Unit (GPU) and the Intel Phi are two examples of such accelerators. Accelerators offer peak performances that can be well above those of the host processor. How to exploit this heterogeneous environment for legacy application codes is not, however, straightforward. This paper considers how matrix operations in typical quantum chemical calculations can be migrated to the GPU and Phi systems. Double precision general matrix multiply operations are endemic in electronic structure calculations, especially methods that include electron correlation, such as density functional theory, second order perturbation theory, and coupled cluster theory. The use of approaches that automatically determine whether to use the host or an accelerator, based on problem size, is explored, with computations that are occurring on the accelerator and/or the host. For data-transfers over PCI-e, the GPU provides the best overall performance for data sizes up to 4096 MB with consistent upload and download rates between 5-5.6 GB/s and 5.4-6.3 GB/s, respectively. The GPU outperforms the Phi for both square and nonsquare matrix multiplications.
Institute of Scientific and Technical Information of China (English)
LI Jian; SONG Dan-Jie; GUO Xiao-Jing; JING Bo
2012-01-01
In order to transmit secure messages,a quantum secure direct communication protocol based on a five-particle cluster state and classical XOR operation is presented.The five-particle cluster state is used to detect eavesdroppers,and the classical XOR operation serving as a one-time-pad is used to ensure the security of the protocol.In the security analysis,the entropy theory method is introduced,and three detection strategies are compared quantitatively by using the constraint between the information that the eavesdroppers can obtain and the interference introduced.If the eavesdroppers intend to obtain all the information,the detection rate of the original ping-pong protocol is 50％; the second protocol,using two particles of the Einstein-PodolskyRosen pair as detection particles,is also 50％; while the presented protocol is 89％.Finally,the security of the proposed protocol is discussed,and the analysis results indicate that the protocol in this paper is more secure than the other two.
Abrams, D.; Williams, C.
1999-01-01
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
Institute of Scientific and Technical Information of China (English)
Qin Han; Hongling Peng; Ronghan Wu; Zhichuan Niu; Haiqiao Ni; Shiyong Zhang; Xiaohong Yang; Yun Du; Cunzhu Tong; Huan Zhao; Yingqiang Xu
2006-01-01
@@ Continuous wave operation of a semiconductor laser diode based on five stacks of InAs quantum dots (QDs) embedded within strained InGaAs quantum wells as an active region is demonstrated. At room temperature, 355-Mw output power at ground state of 1.33-1.35μm for a 20-μm ridge-waveguide laser without facet coating is achieved. By optimizing the molecular beam epitaxy (MBE) growth conditions,the QD density per layer is raised to 4 × 1010 cm-2. The laser keeps lasing at ground state until the temperature reaches 65 ℃.
Karni, Ouri; Capua, Amir; Eisenstein, Gadi; Sichkovskyi, Vitalii; Ivanov, Vitalii; Reithmaier, Johann Peter
2013-11-04
We report direct observations of Rabi oscillations and self-induced transparency in a quantum dot optical amplifier operating at room temperature. The experiments make use of pulses whose durations are shorter than the coherence time which are characterized using Cross-Frequency-Resolved Optical Gating. A numerical model which solves the Maxwell and Schrödinger equations and accounts for the inhomogeneously broadened nature of the quantum dot gain medium confirms the experimental results. The model is also used to explain the relationship between the observability of Rabi oscillations, the pulse duration and the homogeneous and inhomogeneous spectral widths of the semiconductor.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2017-04-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Blind Quantum Signature with Blind Quantum Computation
Li, Wei; Shi, Ronghua; Guo, Ying
2016-12-01
Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.
Rational quantum integrable systems of DN type with polarized spin reversal operators
Directory of Open Access Journals (Sweden)
B. Basu-Mallick
2015-09-01
Full Text Available We study the spin Calogero model of DN type with polarized spin reversal operators, as well as its associated spin chain of Haldane–Shastry type, both in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and the partition function of the former model in closed form, from which we derive an exact formula for the chain's partition function in terms of products of partition functions of Polychronakos–Frahm spin chains of type A. Using a recursion relation for the latter partition functions that we derive in the paper, we are able to numerically evaluate the partition function, and thus the spectrum, of the DN-type spin chain for relatively high values of the number of spins N. We analyze several global properties of the chain's spectrum, such as the asymptotic level density, the distribution of consecutive spacings of the unfolded spectrum, and the average degeneracy. In particular, our results suggest that this chain is invariant under a suitable Yangian group, and that its spectrum coincides with that of a Yangian-invariant vertex model with linear energy function and dispersion relation.
Converting Coherence to Quantum Correlations.
Ma, Jiajun; Yadin, Benjamin; Girolami, Davide; Vedral, Vlatko; Gu, Mile
2016-04-22
Recent results in quantum information theory characterize quantum coherence in the context of resource theories. Here, we study the relation between quantum coherence and quantum discord, a kind of quantum correlation which appears even in nonentangled states. We prove that the creation of quantum discord with multipartite incoherent operations is bounded by the amount of quantum coherence consumed in its subsystems during the process. We show how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.
Shirao, Mizuki; Sato, Takashi; Sato, Noriaki; Nishiyama, Nobuhiko; Arai, Shigehisa
2012-02-13
Room-temperature pulsed operation of a 1.3-µm wavelength transistor laser (TL), consisting of a buried heterostructure (BH) with an npn configuration and an AlGaInAs/InP multiple-quantum-well (MQW) active region, was successfully attained. A threshold base current of 18 mA (threshold emitter current of 150 mA) was obtained with a stripe width of 1.3 µm and a cavity length of 500 µm. The transistor activity as well as the lasing operation were achieved at the same time, which is essential for the high-speed operation of TLs.
Quantum spectral curve for arbitrary state/operator in AdS{sub 5}/CFT{sub 4}
Energy Technology Data Exchange (ETDEWEB)
Gromov, Nikolay [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); St.Petersburg INP,Gatchina, 188 300, St.Petersburg (Russian Federation); Kazakov, Vladimir [LPT, École Normale Superieure,24, rue Lhomond 75005 Paris (France); Université Paris-VI,Place Jussieu, 75005 Paris (France); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ08540 (United States); Leurent, Sébastien [Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS,Université de Bourgogne, 9 avenue Alain Savary, 21000 DIJON (France); Volin, Dmytro [Nordita KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); School of Mathematics, Trinity College Dublin,College Green, Dublin 2 (Ireland)
2015-09-28
We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.
Energy Technology Data Exchange (ETDEWEB)
Rengstl, U.; Schwartz, M.; Herzog, T.; Hargart, F.; Paul, M.; Portalupi, S. L.; Jetter, M.; Michler, P., E-mail: p.michler@ihfg.uni-stuttgart.de [Institut für Halbleiteroptik und Funktionelle Grenzflächen and Research Center SCoPE, University of Stuttgart, Allmandring 3, 70569 Stuttgart (Germany)
2015-07-13
We present an on-chip beamsplitter operating on a single-photon level by means of a quasi-resonantly driven InGaAs/GaAs quantum dot. The single photons are guided by rib waveguides and split into two arms by an evanescent field coupler. Although the waveguides themselves support the fundamental TE and TM modes, the measured degree of polarization (∼90%) reveals the main excitation and propagation of the TE mode. We observe the preserved single-photon nature of a quasi-resonantly excited quantum dot by performing a cross-correlation measurement on the two output arms of the beamsplitter. Additionally, the same quantum dot is investigated under resonant excitation, where the same splitting ratio is observed. An autocorrelation measurement with an off-chip beamsplitter on a single output arm reveal the single-photon nature after evanescent coupling inside the on-chip splitter. Due to their robustness, adjustable splitting ratio, and their easy implementation, rib waveguide beamsplitters with embedded quantum dots provide a promising step towards fully integrated quantum circuits.
Single semiconductor quantum dots
Energy Technology Data Exchange (ETDEWEB)
Michler, Peter (ed.) [Stuttgart Univ. (Germany). Inst. fuer Halbleiteroptik und Funktionelle Grenzflaechen
2009-07-01
This book reviews recent advances in the exciting and rapidly growing field of semiconductor quantum dots via contributions from some of the most prominent researchers in the scientific community. Special focus is given to optical, quantum optical, and spin properties of single quantum dots due to their potential applications in devices operating with single electron spins and/or single photons. This includes single and coupled quantum dots in external fields, cavity-quantum electrodynamics, and single and entangled photon pair generation. Single Semiconductor Quantum Dots also addresses growth techniques to allow for a positioned nucleation of dots as well as applications of quantum dots in quantum information technologies. (orig.)
Ben Bakir, Badhise; Seassal, Christian; Letartre, Xavier; Regreny, Philippe; Gendry, Michel; Viktorovitch, Pierre; Zussy, Marc; Di Cioccio, Léa; Fedeli, Jean-Marc
2006-10-02
The authors report on the design, fabrication and operation of heterogeneous and compact "2.5 D" Photonic Crystal microlaser with a single plane of InAs quantum dots as gain medium. The high quality factor photonic structures are tailored for vertical emission. The devices consist of a top two-dimensional InP Photonic Crystal Slab, a SiO(2) bonding layer, and a bottom high index contrast Si/SiO(2) Bragg mirror deposited on a Si wafer. Despite the fact that no more than about 5% of the quantum dots distribution effectively contribute to the modal gain, room-temperature lasing operation, around 1.5 microm, was achieved by photopumping. A low effective threshold, on the order of 350 microW, and a spontaneous emission factor, over 0.13, could be deduced from experiments.
Duality quantum algorithm efficiently simulates open quantum systems
Shi-Jie Wei; Dong Ruan; Gui-Lu Long
2016-01-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the op...
Energy Technology Data Exchange (ETDEWEB)
Endres, Sebastian; Steiner, Frank, E-mail: sebastian.endres@uni-ulm.d, E-mail: frank.steiner@uni-ulm.d [Institut fuer Theoretische Physik, Universitaet Ulm Albert-Einstein-Allee 11, 89081 Ulm (Germany)
2010-03-05
The Berry-Keating operator H{sub BK} := -i h-bar (x d/dx + 1/2) (Berry and Keating 1999 SIAM Rev. 41 236) governing the Schroedinger dynamics is discussed in the Hilbert space L{sup 2}(R{sub >},dx) and on compact quantum graphs. It has been proved that the spectrum of H{sub BK} defined on L{sup 2}(R{sub >},dx) is purely continuous and thus this quantization of H{sub BK} cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of H{sub BK} acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of H{sub BK}. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the 'squared' Berry-Keating operator H{sub BK}{sup 2} := -x{sup 2} d{sup 2}/dx{sup 2} -2x d/dx - 1/4 which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for H{sup 2}{sub BK} on compact quantum graphs. While the spectra of both H{sub BK} and H{sup 2}{sub BK} on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither H{sub BK} nor H{sup 2}{sub BK} can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2009-01-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e., joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Energy Technology Data Exchange (ETDEWEB)
Rodgers, P
1998-03-01
There is more to information than a string of ones and zeroes the ability of ''quantum bits'' to be in two states at the same time could revolutionize information technology. In the mid-1930s two influential but seemingly unrelated papers were published. In 1935 Einstein, Podolsky and Rosen proposed the famous EPR paradox that has come to symbolize the mysteries of quantum mechanics. Two years later, Alan Turing introduced the universal Turing machine in an enigmatically titled paper, On computable numbers, and laid the foundations of the computer industry one of the biggest industries in the world today. Although quantum physics is essential to understand the operation of transistors and other solid-state devices in computers, computation itself has remained a resolutely classical process. Indeed it seems only natural that computation and quantum theory should be kept as far apart as possible surely the uncertainty associated with quantum theory is anathema to the reliability expected from computers? Wrong. In 1985 David Deutsch introduced the universal quantum computer and showed that quantum theory can actually allow computers to do more rather than less. The ability of particles to be in a superposition of more than one quantum state naturally introduces a form of parallelism that can, in principle, perform some traditional computing tasks faster than is possible with classical computers. Moreover, quantum computers are capable of other tasks that are not conceivable with their classical counterparts. Similar breakthroughs in cryptography and communication followed. (author)
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article,we make a review on the development of a newly proposed quantum computer,duality computer,or the duality quantum computer and the duality mode of quantum computers.The duality computer is based on the particle-wave duality principle of quantum mechanics.Compared to an ordinary quantum computer,the duality quantum computer is a quantum computer on the move and passing through a multi-slit.It offers more computing operations than is possible with an ordinary quantum computer.The most two distinct operations are:the quantum division operation and the quantum combiner operation.The division operation divides the wave function of a quantum computer into many attenuated,and identical parts.The combiner operation combines the wave functions in different parts into a single part.The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer.The main structure of duality quantum computer and duality mode,the duality mode,their mathematical description and algorithm designs are reviewed.
Haggard, Hal M.; Muxin Han; Wojciech Kamiński; Aldo Riello
2015-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat co...
Classical and Quantum Polyhedra
Schliemann, John
2014-01-01
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum polyhedra. Regarding tetrahedra, we compare the results from a canonical quantization of the classical system with a recent wave function based approach to the large-volume sector of the quantum system. Both methods agree in the leading order of the resulting effective operator (given by an harmonic oscillator), while minor differences occur in higher corrections. Perturbative inclusion of such corrections improves the approximation to the eigenstates. Moreover, the comparison of both methods leads also to a full wave function description of the eigenstates of the (square of the) volume operator at negative eigenvalues of large modulus. For the case of general quantum polyhedra described by discrete angular momentum quantum numbers we formulate a set of quantum operators fulfill...
Quantum probability and quantum decision-making.
Yukalov, V I; Sornette, D
2016-01-13
A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.
Rapoport, Diego L.
2011-01-01
In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation
量子与经典对应：Dirac方程中的速度算符%Quantum and classical correspondence for velocity operator in Dirac equation
Institute of Scientific and Technical Information of China (English)
张治国; 封文江; 郑伟; 陈皓; 崔崧
2016-01-01
Due to Bohr correspondence principle in the quantum mechanics,quantum mechanics go to classical mechanics in the case of large quantum number. Based upon Heisenberg correspondence principle, quantum matrix element of a Hermitian operator reduces to the coefficient of Fourier expansion of the corresponding classical quantity in the classical limit.Using Heisenberg correspondence principle, quantum-classical correspondence of the relativistic free particle and the 1/2 spin charged particles in a constant magnetic field are studied.Applying Heisenberg correspondence principle to Dirac equation in relativistic realm,the operator of free particle in the Dirac theory and quantum-classical correspondence are obtained,and 1/2 spin charged particle in a constant magnetic field in Dirac equation is also studied.For the relativistic free particle or the charged particle in a constant magnetic field,the velocity operator in the Dirac theory will reduce to the classical velocity.%由量子力学中的Bohr对应原理可知,在大量子数情形下,量子力学应过渡到经典力学。在经典极限下,由 Heisenberg 对应原理可知,厄密算符的量子矩阵元对应经典物理量的Fourier展开系数。利用 Heisenberg对应原理研究相对论效应的自由粒子和在匀磁场中的带电粒子的量子经典对应问题。将 Heisenberg对应原理应用到相对论领域的 Dirac 方程,计算出自由粒子的Dirac方程中的α算符及其经典近似,并且研究自旋1/2的带电粒子在匀磁场中的Dirac 方程情形。对于相对论效应的自由粒子和在匀磁场中的带电粒子,Dirac理论中的α算符将对应经典的速度。
Lazur, V. Yu.; Myhalyna, S. I.; Reity, O. K.
The problem of interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. The interaction is considered as a second-order effect of quantum electrodynamics in the coordinate representation. It is shown that a consistent account for the natural condition of the interaction symmetry with respect to both electrons leads to an additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator known previously. The generalized Breit-Pauli operator and the operator of electric dipole-dipole interaction of two quasimolecular electrons located at an arbitrary distance from each other are obtained. Modern methods of accounting for the relativistic and correlative effects in the problem of ion-atom interactions are discussed.
Cheon, Taksu; Tsutsui, Izumi; Fülöp, Tamás
2004-09-01
We show that the point interactions on a line can be utilized to provide U(2) family of qubit operations for quantum information processing. Qubits are realized as states localized in either side of the point interaction which represents a controllable gate. The qubit manipulation proceeds in a manner analogous to the operation of an abacus.
Quantum State Tomography and Quantum Games
Institute of Scientific and Technical Information of China (English)
Ahmad Nawaz
2012-01-01
A technique is developed for single qubit quantum state tomography using the mathematical setup of generalized quantization scheme for games. In this technique,Alice sends an unknown pure quantum state to Bob who appends it with |0><0| and then applies the unitary operators on the appended quantum state and finds the payoffs for Alice and himself.It is shown that for a particular set of unitary operators,these payoffs are equal to Stokes parameters for an unknown quantum state.In this way an unknown quantum state can be measured and reconstructed.Strictly speaking,this technique is not a game as no strategic competitions are involved.
Curran, Stephen
2009-01-01
In arXiv:0807.0677, K\\"ostler and Speicher observed that de Finetti's theorem on exchangeable sequences has a free analogue if one replaces exchangeability by the stronger condition of invariance under quantum permutations. In this paper we study sequences of noncommutative random variables whose joint distribution is invariant under quantum orthogonal transformations. We prove a free analogue of Freedman's characterization of conditionally independent Gaussian families, namely an infinite sequence of self-adjoint random variables is quantum orthogonally invariant if and only if they form an operator-valued free centered equivariant semicircular family. Similarly, we show that an infinite sequence of noncommutative random variables is quantum unitarily invariant if and only if they form an operator-valued free centered equivariant circular family. We provide an example to show that, as in the classical case, these results fail for finite sequences. We then give an approximation to how far the distribution of ...
Gudder, Stanley P
2014-01-01
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the ne
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
Nanophotonic quantum computer based on atomic quantum transistor
Energy Technology Data Exchange (ETDEWEB)
Andrianov, S N [Institute of Advanced Research, Academy of Sciences of the Republic of Tatarstan, Kazan (Russian Federation); Moiseev, S A [Kazan E. K. Zavoisky Physical-Technical Institute, Kazan Scientific Center, Russian Academy of Sciences, Kazan (Russian Federation)
2015-10-31
We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)
Alvarez-Rodriguez, U; Lamata, L; Solano, E
2014-01-01
Addition plays a central role in mathematics and physics, while adders are ubiquitous devices in computation and electronics. In this sense, usual sum operations can be realized by classical Turing machines and also, with a suitable algorithm, by quantum Turing machines. Moreover, the sum of state vectors in the same Hilbert space, known as quantum superposition, is at the core of quantum physics. In fact, entanglement and the promised exponential speed-up of quantum computing are based on such superpositions. Here, we consider the existence of a quantum adder, defined as a unitary operation mapping two unknown quantum states encoded in different quantum systems onto their sum codified in a single one. The surprising answer is that this quantum adder is forbidden and it has the quantum cloning machine as a special case. This no-go result is of fundamental nature and its deep implications should be further studied.
Efficient Quantum Pseudorandomness
Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał
2016-04-01
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.
Efficient Quantum Pseudorandomness.
Brandão, Fernando G S L; Harrow, Aram W; Horodecki, Michał
2016-04-29
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.
Mehmannavaz, Mohammad Reza; Sattari, Hamed
2014-12-01
We investigate the light amplification and gain without inversion (GWI) in triple quantum dot molecules in both steady-state and transient state. We demonstrate that the light amplification and GWI of a light pulse can be controlled through the rates of the incoherent pumping and tunneling between electronic levels. The required switching times for switching of a light pulse from absorption to gain and vice versa is then discussed. We obtain switching time at about 40 ps, which resembles a high-speed optical switch in nanostructure. The proposed approach in QDMs may provide some new possibilities for technological applications in optoelectronics and solid-state quantum information science.
Ness, H
2013-08-01
In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.
Introduction to quantum information science
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Masahito [Nagoya Univ. (Japan). Graduate School of Mathematics; Ishizaka, Satoshi [Hiroshima Univ., Higashi-Hiroshima (Japan). Graduate School of Integrated Arts and Sciences; Kawachi, Akinori [Tokyo Institute of Technology (Japan). Dept. of Mathematical and Computing Sciences; Kimura, Gen [Shibaura Institute of Technology, Saitama (Japan). College of Systems Engineering and Science; Ogawa, Tomohiro [Univ. of Electro-Communications, Tokyo (Japan). Graduate School of Information Systems
2015-04-01
Presents the mathematical foundation for quantum information in a very didactic way. Summarizes all required mathematical knowledge in linear algebra. Supports teaching and learning with more than 100 exercises with solutions. Includes brief descriptions to recent results with references. This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error
Quantum Robots Plus Environments
Benioff, P
1998-01-01
A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and physical experiments on the environment. Environments considered so far in the literature: oracles, data bases, and quantum registers, are shown to be special cases of environments considered here. It is noted that quantum robots should include a quantum computer and cannot be simply a multistate head. A model is discussed in which each task, as a sequence of computation and action phases, is described by a unitary step operator. Overall system dynamics is described in terms of a Feynman sum over paths of completed computation and action phases. A simple task example, measuring the distance between the quantum robot and a particle on a 1D space lattice, with quantum phase path and time duration dispersion present, is analyzed.
Endres, Sebastian
2009-01-01
The Berry-Keating operator $H_{\\mathrm{BK}}:= -\\ui\\hbar(x\\frac{\\ud\\phantom{x}}{\\ud x}+{1/2})$ [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\\"odinger dynamics is discussed in the Hilbert space $L^2(\\rz_>,\\ud x)$ and on compact quantum graphs. It is proved that the spectrum of $H_{\\mathrm{BK}}$ defined on $L^2(\\rz_>,\\ud x)$ is purely continuous and thus this quantization of $H_{\\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the ``squared'' Berry-Keating operator $H_{\\mathrm{BK}}^2:= -x^2\\frac{\\ud^2...
Patel, Tushita; Klanian, Kelly; Gong, Zongyi; Williams, Mark B
2012-07-01
The spatial frequency dependent detective quantum efficiency (DQE) of a CsI-CMOS x-ray detector was measured in two operating modes: a high dynamic range (HDR) mode and a high sensitivity (HS) mode. DQE calculations were performed using the IEC-62220-1-2 Standard. For detector entrance air kerma values between ~7 µGy and 60 µGy the DQE is similar in either HDR mode or HS mode, with a value of ~0.7 at low frequency and ~ 0.15 - 0.20 at the Nyquist frequency fN = 6.7 mm(-1). In HDR mode the DQE remains virtually constant for operation with Ka values between ~7 µGy and 119 µGy but decreases for Ka levels below ~ 7 µGy. In HS mode the DQE is approximately constant over the full range of entrance air kerma tested between 1.7 µGy and 60 µGy but kerma values above ~75 µGy produce hard saturation. Quantum limited operation in HS mode for entrance kerma as small as 1.7 µGy makes it possible to use a large number of low dose views to improve angular sampling and decrease acquisition time.
Institute of Scientific and Technical Information of China (English)
陈光巨; 李玉学
1999-01-01
The concrete molecule-fixed （MF） kinetic energy operator for penta-atomic molecules is expressed in terms of the parameterδ, the matrix element G?, and angular momentum operator （?）. The applications of the operator are also discussed. Finally, a general compact form of kinetic energy operator suitable for calculating the rovibrational spectra of polyatomie molecules is presented.
Unitary equivalence of quantum walks
Energy Technology Data Exchange (ETDEWEB)
Goyal, Sandeep K., E-mail: sandeep.goyal@ucalgary.ca [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, 4000 Durban (South Africa); Konrad, Thomas [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, 4000 Durban (South Africa); National Institute for Theoretical Physics (NITheP), KwaZulu-Natal (South Africa); Diósi, Lajos [Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest 114, P.O.B. 49 (Hungary)
2015-01-23
Highlights: • We have found unitary equivalent classes in coined quantum walks. • A single parameter family of coin operators is sufficient to realize all simple one-dimensional quantum walks. • Electric quantum walks are unitarily equivalent to time dependent quantum walks. - Abstract: A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.
Li, Fushan; Son, Dong Ick; Cho, Sung Hwan; Kim, Tae Whan
2009-05-01
Transmission electron microscopy images showed that the ZnO quantum dots (QDs) were conjugated with multi-walled carbon nanotubes (MWCNTs). Bistable memories utilizing an ensemble of the ZnO QD-MWCNT heterostructures were developed and the storage capability of the devices was significantly enhanced due to the conjugation of the ZnO QDs and the MWCNTs. Operating mechanisms of memory devices fabricated utilizing the ZnO QD-MWCNT heterostructures are described on the basis of the current-voltage results. The memory devices exhibited excellent environmental stability at ambient conditions.
Miki, Kei
2016-07-01
Highest weight modules for U q ( g l 2 ̂ ) are endowed with a structure of modules for the quantum toriodal algebra U κ of type sl2. Using this, we define U κ actions on the space of vertex operators for irreducible highest weight U q ( g l 2 ̂ ) modules. Highest or lowest weight vectors of the thus obtained U κ modules are expressed in terms of an intertwiner for U q ( s l 2 ̂ ) modules and an extra boson. The submodules generated by these vectors are investigated.
Advanced quantum communication systems
Jeffrey, Evan Robert
Quantum communication provides several examples of communication protocols which cannot be implemented securely using only classical communication. Currently, the most widely known of these is quantum cryptography, which allows secure key exchange between parties sharing a quantum channel subject to an eavesdropper. This thesis explores and extends the realm of quantum communication. Two new quantum communication protocols are described. The first is a new form of quantum cryptography---relativistic quantum cryptography---which increases communication efficiency by exploiting a relativistic bound on the power of an eavesdropper, in addition to the usual quantum mechanical restrictions intrinsic to quantum cryptography. By doing so, we have observed over 170% improvement in communication efficiency over a similar protocol not utilizing relativity. A second protocol, Quantum Orienteering, allows two cooperating parties to communicate a specific direction in space. This application shows the possibility of using joint measurements, or projections onto an entangled state, in order to extract the maximum useful information from quantum bits. For two-qubit communication, the maximal fidelity of communication using only separable operations is 73.6%, while joint measurements can improve the efficiency to 78.9%. In addition to implementing these protocols, we have improved several resources for quantum communication and quantum computing. Specifically, we have developed improved sources of polarization-entangled photons, a low-loss quantum memory for polarization qubits, and a quantum random number generator. These tools may be applied to a wide variety of future quantum and classical information systems.
An algorithm for minimization of quantum cost
Banerjee, Anindita; Pathak, Anirban
2009-01-01
A new algorithm for minimization of quantum cost of quantum circuits has been designed. The quantum cost of different quantum circuits of particular interest (eg. circuits for EPR, quantum teleportation, shor code and different quantum arithmetic operations) are computed by using the proposed algorithm. The quantum costs obtained using the proposed algorithm is compared with the existing results and it is found that the algorithm has produced minimum quantum cost in all cases.
Quantum Simulation of Phylogenetic Trees
Ellinas, Demosthenes
2011-01-01
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic phylogenetic models applying on trees of various topologies are simulated following appropriate decoherent quantum circuits. Quantum simulations of statistical inference for aligned sequences of biological characters are provided in terms of a quantum pruning map operating on likelihood operator observables, utilizing state-observable duality and measurement theory.
Quantum thermodynamics of general quantum processes.
Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John
2015-03-01
Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics.
Jensen, Kasper; Thomas, Rodrigo A; Wang, Tian; Fuchs, Annette; Balabas, Mikhail V; Vasilakis, Georgios; Mosgaard, Lars; Heimburg, Thomas; Olesen, Søren-Peter; Polzik, Eugene S
2016-01-01
Magnetic fields generated by human and animal organs, such as the heart, brain and nervous system carry information useful for biological and medical purposes. These magnetic fields are most commonly detected using cryogenically-cooled superconducting magnetometers. Here we present the frst detection of action potentials from an animal nerve using an optical atomic magnetometer. Using an optimal design we are able to achieve the sensitivity dominated by the quantum shot noise of light and quantum projection noise of atomic spins. Such sensitivity allows us to measure the nerve impulse with a miniature room-temperature sensor which is a critical advantage for biomedical applications. Positioning the sensor at a distance of a few millimeters from the nerve, corresponding to the distance between the skin and nerves in biological studies, we detect the magnetic field generated by an action potential of a frog sciatic nerve. From the magnetic field measurements we determine the activity of the nerve and the tempor...
Streltsov, Alexander
2015-01-01
The basis of any quantum resource theory are free states and free operations, these are states and operations which can be created or performed at no cost. In the resource theory of quantum coherence free states are states which are diagonal in a fixed reference basis. This choice is natural in many experimental scenarios where the reference basis is singled out by the unavoidable decoherence. The corresponding free operations are called incoherent, they can be implemented as a generalized measurement which does not create any coherence. However, a general quantum operation admits different experimental realizations, and a quantum operation which seems incoherent in one experimental realization might create coherence in another. Starting from this observation, we propose the framework of genuine quantum coherence. This approach is based on a simple principle: we demand that a genuinely incoherent operation preserves all incoherent states. This simple condition automatically guarantees that the operation is in...
Quantum Memory as Light Pulses Quantum States Transformer
Directory of Open Access Journals (Sweden)
Vetlugin A.N.
2015-01-01
Full Text Available Quantum memory can operate not only as a write-in/readout device [1] for quantum light pulses and non-classical states generation [2] device but also as a quantum states of light transformer. Here the addressable parallel quantum memory [3] possibilities for this type of transformation are researched. Quantum memory operates as a conventional N-port interferometer with N equals to the number of the involved spin waves. As example we consider the ability to transform quantum states of two light pulses – in this case the quantum memory works as a mirror with a controlled transmission factor.
Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyeon; Choi, Seong-Gon
2016-12-01
We present a scheme for implementing discrete quantum Fourier transform (DQFT) with robustness against the decoherence effect using weak cross-Kerr nonlinearities (XKNLs). The multi-photon DQFT scheme can be achieved by operating the controlled path and merging path gates that are formed with weak XKNLs and linear optical devices. To enhance feasibility under the decoherence effect, in practice, we utilize a displacement operator and photon-number-resolving measurement in the optical gate using XKNLs. Consequently, when there is a strong amplitude of the coherent state, we demonstrate that it is possible to experimentally implement the DQFT scheme, utilizing current technology, with a certain probability of success under the decoherence effect.
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Testing Nonassociative Quantum Mechanics.
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-27
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
The quantum Arnold transformation
Aldaya, V.; Cossío, F.; Guerrero, J.; López-Ruiz, F. F.
2011-02-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with friction linear in velocity, can be related to the quantum free-particle dynamical system. This transformation provides a basic (Heisenberg-Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schrödinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wavefunctions and closed analytic expressions for time-evolution operators.
Institute of Scientific and Technical Information of China (English)
陈光巨; 刘若庄
1996-01-01
The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.
Role of quantum discord in quantum communication
Madhok, Vaibhav
2011-01-01
Positivity of quantum discord is shown to be equivalent to the strong sub additivity of the Von-Nuemann entropy. This leads to a connection between the mother protocol of quantum information theory [A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537, (2009)] and quantum discord. We exploit this to show that quantum discord is a measure coherence in the performance of the mother protocol. Since the mother protocol is a unification of an important class of problems (those that are bipartite, unidirectional and memoryless), we show quantum discord to be a measure of coherence in these protocols. Our work generalizes an earlier operational interpretation of quantum discord provided in terms of quantum state merging [V. Madhok and A. Datta, Phys. Rev. A 83, 032323, (2011)].
Fundamentals of quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Klauder, J R [Department of Physics and Department of Mathematics, University of Florida, Gainesville FL 32611-8440 (United States)
2007-11-15
The outline of a recent approach to quantum gravity is presented. Novel ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach toward quantum constraints; (4) Continuous-time regularized functional integral representation without/with constraints; and (5) Hard core picture of nonrenormalizability. The 'diagonal representation' for operator representations, introduced by Sudarshan into quantum optics, arises naturally within this program.
Jensen, Kasper; Budvytyte, Rima; Thomas, Rodrigo A.; Wang, Tian; Fuchs, Annette M.; Balabas, Mikhail V.; Vasilakis, Georgios; Mosgaard, Lars D.; Stærkind, Hans C.; Müller, Jörg H.; Heimburg, Thomas; Olesen, Søren-Peter; Polzik, Eugene S.
2016-07-01
Magnetic fields generated by human and animal organs, such as the heart, brain and nervous system carry information useful for biological and medical purposes. These magnetic fields are most commonly detected using cryogenically-cooled superconducting magnetometers. Here we present the first detection of action potentials from an animal nerve using an optical atomic magnetometer. Using an optimal design we are able to achieve the sensitivity dominated by the quantum shot noise of light and quantum projection noise of atomic spins. Such sensitivity allows us to measure the nerve impulse with a miniature room-temperature sensor which is a critical advantage for biomedical applications. Positioning the sensor at a distance of a few millimeters from the nerve, corresponding to the distance between the skin and nerves in biological studies, we detect the magnetic field generated by an action potential of a frog sciatic nerve. From the magnetic field measurements we determine the activity of the nerve and the temporal shape of the nerve impulse. This work opens new ways towards implementing optical magnetometers as practical devices for medical diagnostics.
Jensen, Kasper; Budvytyte, Rima; Thomas, Rodrigo A; Wang, Tian; Fuchs, Annette M; Balabas, Mikhail V; Vasilakis, Georgios; Mosgaard, Lars D; Stærkind, Hans C; Müller, Jörg H; Heimburg, Thomas; Olesen, Søren-Peter; Polzik, Eugene S
2016-07-15
Magnetic fields generated by human and animal organs, such as the heart, brain and nervous system carry information useful for biological and medical purposes. These magnetic fields are most commonly detected using cryogenically-cooled superconducting magnetometers. Here we present the first detection of action potentials from an animal nerve using an optical atomic magnetometer. Using an optimal design we are able to achieve the sensitivity dominated by the quantum shot noise of light and quantum projection noise of atomic spins. Such sensitivity allows us to measure the nerve impulse with a miniature room-temperature sensor which is a critical advantage for biomedical applications. Positioning the sensor at a distance of a few millimeters from the nerve, corresponding to the distance between the skin and nerves in biological studies, we detect the magnetic field generated by an action potential of a frog sciatic nerve. From the magnetic field measurements we determine the activity of the nerve and the temporal shape of the nerve impulse. This work opens new ways towards implementing optical magnetometers as practical devices for medical diagnostics.
Fluxon-controlled quantum computer
Fujii, Toshiyuki; Matsuo, Shigemasa; Hatakenaka, Noriyuki
2016-11-01
We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e. joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.
Behbahani, Mina Morshed; Mahdifar, Ali
2016-01-01
As a probe to explore the ability of invisibility cloaks to conceal objects in the quantum mechanics domain, we study the spontaneous emission rate of an excited two-level atom in the vicinity of an ideal invisibility cloaking. On this base, first, a canonical quantization scheme is presented for the electromagnetic field interacting with atomic systems in an anisotropic, inhomogeneous and absorbing magnetodielectric medium which can suitably be used for studying the influence of arbitrary invisibility cloak on the atomic radiative properties. The time dependence of the atomic subsystem is obtained in the Schrodinger picture. By introducing a modified set of the spherical wave vector functions, the Green tensor of the system is calculated via the continuous and discrete methods. In this formalism, the decay rate and as well the emission pattern of the aforementioned atom are computed analytically for both weak and strong coupling interaction, and then numerically calculations are done to demonstrate the perfo...
Distributed feedback quantum cascade lasers operating in continuous-wave mode at λ ≈ 7.6 μm
Jinchuan, Zhang; Lijun, Wang; Wanfeng, Liu; Fengqi, Liu; Lihua, Zhao; Shenqiang, Zhai; Junqi, Liu; Zhanguo, Wang
2012-02-01
Distributed feedback (DFB) quantum cascade lasers (QCLs) in continuous-wave (CW) mode emitting at λ ≈ 7.6 μm are presented. Holographic lithography was used to fabricate the first-order distributed feedback grating. For a high-reflectivity-coated QCL with 14.5-μm-wide and 3-mm-long cavity, CW output powers of 300 mW at 85 K and still 10 mW at 270 K are obtained. Single-mode emission with a side-mode suppression ratio (SMSR) of about 30 dB and a wide tuning range of ~300 nm in the temperature range from 85 to 280 K is observed.
Yousefvand, Hossein Reza
2017-07-01
In this paper a self-consistent numerical approach to study the temperature and bias dependent characteristics of mid-infrared (mid-IR) quantum cascade lasers (QCLs) is presented which integrates a number of quantum mechanical models. The field-dependent laser parameters including the nonradiative scattering times, the detuning and energy levels, the escape activation energy, the backfilling excitation energy and dipole moment of the optical transition are calculated for a wide range of applied electric fields by a self-consistent solution of Schrodinger-Poisson equations. A detailed analysis of performance of the obtained structure is carried out within a self-consistent solution of the subband population rate equations coupled with carrier coherent transport equations through the sequential resonant tunneling, by taking into account the temperature and bias dependency of the relevant parameters. Furthermore, the heat transfer equation is included in order to calculate the carrier temperature inside the active region levels. This leads to a compact predictive model to analyze the temperature and electric field dependent characteristics of the mid-IR QCLs such as the light-current (L-I), electric field-current (F-I) and core temperature-electric field (T-F) curves. For a typical mid-IR QCL, a good agreement was found between the simulated temperature-dependent L-I characteristic and experimental data, which confirms validity of the model. It is found that the main characteristics of the device such as output power and turn-on delay time are degraded by interplay between the temperature and Stark effects.
Quantum Robots and Environments
Benioff, P
1998-01-01
Quantum robots and their interactions with environments of quantum systems are described and their study justified. A quantum robot is a mobile quantum system that includes a quantum computer and needed ancillary systems on board. Quantum robots carry out tasks whose goals include specified changes in the state of the environment or carrying out measurements on the environment. Each task is a sequence of alternating computation and action phases. Computation phase activities include determination of the action to be carried out in the next phase and possible recording of information on neighborhood environmental system states. Action phase activities include motion of the quantum robot and changes of neighborhood environment system states. Models of quantum robots and their interactions with environments are described using discrete space and time. To each task is associated a unitary step operator T that gives the single time step dynamics. T = T_{a}+T_{c} is a sum of action phase and computation phase step ...
Ahn, Doyeol
2011-01-01
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...
Problems and solutions in quantum computing and quantum information
Steeb, Willi-Hans
2012-01-01
Quantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest. This book supplies a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. All the important concepts and topics such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, deportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, number states and Bose operators, coherent states, squeezed states, Gaussian states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton opera...
Quantum chaos in quantum Turing machines
Kim, I; Kim, Ilki; Mahler, Guenter
1999-01-01
We investigate a 2-spin quantum Turing architecture, in which discrete local rotations $\\alpha_m$ of the Turing head spin alternate with quantum controlled NOT-opera-\\linebreak%%operations tions. We demonstrate that a single chaotic parameter input $\\alpha_m$ leads to a chaotic dynamics in the entire Hilbert-space.
DEFF Research Database (Denmark)
Semenova, Elizaveta; Kulkova, Irina; Kadkhodazadeh, Shima
2014-01-01
The development of epitaxial technology for the fabrication of quantum dot (QD) gain material operating in the 1.55 μm wavelength range is a key requirement for the evolvement of telecommunication. High performance QD material demonstrated on GaAs only covers the wavelength region 1-1.35 μm...... lithography. Due to the lower lattice mismatch of InAs/InP compared to InAs/GaAs, InP based QDs have a larger diameter and are shallower compared to GaAs based dots. This shape causes low carrier localization and small energy level separation which leads to a high threshold current, high temperature...... with the possibility to approach an ideal QD shape....
Directory of Open Access Journals (Sweden)
H. Oda
2016-06-01
Full Text Available The development of small sized laser operating above room temperature is important in the realization of optical integrated circuits. Recently, micro-lasers consisting of photonic crystals (PhCs and whispering gallery mode cavities have been demonstrated. Optically pumped laser devices could be easily designed using photonic crystal-slab waveguides (PhC-WGs with an air-bridge type structure. In this study, we observe lasing at 1.3μm from two-photon pumped InAs-quantum-dots embedded GaAs PhC-WGs above room temperature. This type of compact laser shows promise as a new light source in ultra-compact photonics integrated circuits.
Broad area quantum cascade lasers operating in pulsed mode above 100 °C λ ∼4.7 μm
Zhao, Yue; Yan, Fangliang; Zhang, Jinchuan; Liu, Fengqi; Zhuo, Ning; Liu, Junqi; Wang, Lijun; Wang, Zhanguo
2017-07-01
We demonstrate a broad area (400 μm) high power quantum cascade laser (QCL). A total peak power of 62 W operating at room temperature is achieved at λ ∼4.7 μm. The temperature dependence of the peak power characteristic is given in the experiment, and also the temperature of the active zone is simulated by a finite-element-method (FEM). We find that the interface roughness of the active core has a great effect on the temperature of the active zone and can be enormously improved using the solid source molecular beam epitaxy (MBE) growth system. Project supported by the National Basic Research Program of China (No. 2013CB632801), the National Key Research and Development Program (No. 2016YFB0402303), the National Natural Science Foundation of China (Nos. 61435014, 61627822, 61574136, 61306058, 61404131), the Key Projects of Chinese Academy of Sciences (No. ZDRW-XH-20164), and the Beijing Natural Science Foundation (No. 4162060).
Yoshida, Z
2016-01-01
Quantum systems often exhibit fundamental incapability to entertain vortex. The Meissner effect, a complete expulsion of the magnetic field (the electromagnetic vorticity), for instance, is taken to be the defining attribute of the superconducting state. Superfluidity is another, close-parallel example; fluid vorticity can reside only on topological defects with a limited (quantized) amount. Recent developments in the Bose-Einstein condensates produced by particle traps further emphasize this characteristic. We show that the challenge of imparting vorticity to a quantum fluid can be met through a nonlinear mechanism operating in a hot fluid corresponding to a thermally modified Pauli-Schroedinger spinor field. In a simple field-free model, we show that the thermal effect, represented by a nonlinear, non-Hermitian Hamiltonian, in conjunction with spin vorticity, leads to new interesting quantum states; a spiral solution is explicitly worked out.
Exner, Pavel
2015-01-01
This monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
Energy Technology Data Exchange (ETDEWEB)
Pejov, Ljupčo, E-mail: ljupcop@pmf.ukim.mk [Department of Physical Chemistry, Institute of Chemistry, SS. Cyril and Methodius University, Arhimedova 5, P.O. Box 162, 1001 Skopje, Republic of Macedonia (Macedonia, The Former Yugoslav Republic of); Petreska, Irina [Institute of Physics, Faculty of Natural Sciences and Mathematics, SS. Cyril and Methodius University, P.O. Box 162, 1001 Skopje, Republic of Macedonia (Macedonia, The Former Yugoslav Republic of); Kocarev, Ljupčo [Macedonian Academy of Sciences and Arts, Krste Misirkov 2, P.O. Box 428, 1000 Skopje, Republic of Macedonia (Macedonia, The Former Yugoslav Republic of); Faculty of Computer Science and Engineering, SS. Cyril and Methodius University, P.O. Box 393, 100 Skopje, Republic of Macedonia (Macedonia, The Former Yugoslav Republic of); BioCircuits Institute, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0402 (United States)
2015-12-28
A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a “quantum dot”), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1–014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1–245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green’s function formalism, as well as by analysis of frontier molecular orbitals’ behavior.
Haggard, Hal M.; Han, Muxin; Kamiński, Wojciech; Riello, Aldo
2015-11-01
We study the expectation value of a nonplanar Wilson graph operator in SL (2, C) Chern-Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. This can be understood as arising from the relation between Chern-Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL (2, C) Chern-Simons theory in 3 dimensions with knotted graph defects.
Directory of Open Access Journals (Sweden)
Hal M. Haggard
2015-11-01
Full Text Available We study the expectation value of a nonplanar Wilson graph operator in SL(2,C Chern–Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C Chern–Simons theory in 3 dimensions with knotted graph defects.
Pejov, Ljupčo; Petreska, Irina; Kocarev, Ljupčo
2015-12-01
A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a "quantum dot"), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1-014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1-245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green's function formalism, as well as by analysis of frontier molecular orbitals' behavior.
Pejov, Ljupčo; Petreska, Irina; Kocarev, Ljupčo
2015-12-28
A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a "quantum dot"), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1-014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1-245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green's function formalism, as well as by analysis of frontier molecular orbitals' behavior.
Quantum state revivals in quantum walks on cycles
Directory of Open Access Journals (Sweden)
Phillip R. Dukes
2014-01-01
Full Text Available Recurrence in the classical random walk is well known and described by the Pólya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under certain circumstances the quantum walker may also return to an arbitrary initial quantum state in a finite number of steps. Quantum state revivals in quantum walks on cycles using coin operators which are constant in time and uniform across the path have been described before but only incompletely. In this paper we find the general conditions for which full-quantum state revival will occur.
Quantum dynamics as a physical resource
Nielsen, M A; Dodd, J L; Gilchrist, A; Mortimer, D; Osborne, T J; Bremner, M J; Harrow, A W; Hines, A; Nielsen, Michael A.; Dawson, Christopher M.; Dodd, Jennifer L.; Gilchrist, Alexei; Mortimer, Duncan; Osborne, Tobias J.; Bremner, Michael J.; Harrow, Aram W.; Hines, Andrew
2003-01-01
How useful is a quantum dynamical operation for quantum information processing? Motivated by this question we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of such strength measures, based on axiomatic considerations independent of state-based resources. The power of this theory is demonstrated with applications to quantum communication complexity, quantum computational complexity, and entanglement generation by unitary operations.
Experimental repetitive quantum error correction.
Schindler, Philipp; Barreiro, Julio T; Monz, Thomas; Nebendahl, Volckmar; Nigg, Daniel; Chwalla, Michael; Hennrich, Markus; Blatt, Rainer
2011-05-27
The computational potential of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We implement multiple quantum error correction cycles for phase-flip errors on qubits encoded with trapped ions. Errors are corrected by a quantum-feedback algorithm using high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive correction cycles are realized, and the behavior of the algorithm for different noise environments is analyzed.
Gaiotto, Davide
2014-01-01
We reformulate the action of Verlinde line operators on conformal blocks in a 3d TFT language and extend it to line operators labelled by open paths joining punctures on the Riemann surface. We discuss the possible applications of open Verlinde line operators to quantum Teichm\\"uller theory, supersymmetric gauge theory and quantum groups
Quantum Computer Using Coupled Quantum Dot Molecules
Wu, N J; Natori, A; Yasunaga, H; Wu*, Nan-Jian
1999-01-01
We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can...
Directory of Open Access Journals (Sweden)
Yoon SF
2006-01-01
Full Text Available AbstractSelf-assembled GaInNAs quantum dots (QDs were grown on GaAs (001 substrate using solid-source molecular-beam epitaxy (SSMBE equipped with a radio-frequency nitrogen plasma source. The GaInNAs QD growth characteristics were extensively investigated using atomic-force microscopy (AFM, photoluminescence (PL, and transmission electron microscopy (TEM measurements. Self-assembled GaInNAs/GaAsN single layer QD lasers grown using SSMBE have been fabricated and characterized. The laser worked under continuous wave (CW operation at room temperature (RT with emission wavelength of 1175.86 nm. Temperature-dependent measurements have been carried out on the GaInNAs QD lasers. The lowest obtained threshold current density in this work is ∼1.05 kA/cm2from a GaInNAs QD laser (50 × 1,700 µm2 at 10 °C. High-temperature operation up to 65 °C was demonstrated from an unbonded GaInNAs QD laser (50 × 1,060 µm2, with high characteristic temperature of 79.4 K in the temperature range of 10–60 °C.
Haggard, Hal M; Kamiński, Wojciech; Riello, Aldo
2014-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains at the leading order an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged ...
Daumer, Martin; Dürr, Detlef; Goldstein, Sheldon; Zanghì, Nino
1996-01-01
A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about ``measuring operators'' that occurs when the subject is quantum mechanics. Without a specification of what should be meant by ``measuring'' a quantum observable, such an expression can have no clear meaning. A definite specifi...
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Quantum Diffusion, Measurement and Filtering
Belavkin, V P
1993-01-01
A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined. Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition observation are derived. A stochastic equation of quantum diffusion filtering generalising the classical Markov filtering equation to the quantum flows over arbitrary *-algebra is obtained. A Gaussian quantum diffusion with one dimensional continuous observation is considered.The a posteriori quantum state difusion in this case is reduced to a linear quantum stochastic filter equation of Kalman-Bucy type and to the operator Riccati equation for quantum correlations. An example of continuous nondemolition observation of the coordinate of a free quantum particle is considered, describing a continuous collase to the statio...
Zanardi, Paolo
2001-01-01
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\\cal A$ of operationally relevant observables. The algebraic structure of $\\cal A$ selects a preferred tensor product structure i.e., a partition into subsystems. The notion of compoundness for quantum system is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies
Zanardi, P
2001-08-13
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables. The algebraic structure of A selects a preferred tensor product structure, i.e., a partition into subsystems. The notion of compoundness for quantum systems is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies
Open quantum system identification
Schirmer, Sophie G; Zhou, Weiwei; Gong, Erling; Zhang, Ming
2012-01-01
Engineering quantum systems offers great opportunities both technologically and scientifically for communication, computation, and simulation. The construction and operation of large scale quantum information devices presents a grand challenge and a major issue is the effective control of coherent dynamics. This is often in the presence of decoherence which further complicates the task of determining the behaviour of the system. Here, we show how to determine open system Markovian dynamics of a quantum system with restricted initialisation and partial output state information.
Parallelizing quantum circuit synthesis
Di Matteo, Olivia; Mosca, Michele
2016-01-01
Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools which can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in t...
Institute of Scientific and Technical Information of China (English)
宋玉翠; 邱香廷
2009-01-01
Objective To investigate and evaluate the effect of personnel movement frequency during operation to quantum of bacteria in air in laminar flow operation room. Methods Air samples during 20 operation cases were collected by plat slab exposure method. The sampling-time was from starting laminar flow for 30 minutes (patients came into operation room at this time)to operation finish. During this time,samples were taken from the rooms every 30 minutes and persons' movement fre-quency were recorded. Results At each phase,the correlation coeffcient of persons' movement frequency during operation and quantum of bacteria in air in laminar flow operation room was 0. 945. There was correlation between quantum of bacteria in air and persons' movement. Quantum of bacte-ria of air would exceed national sanitary standard of normal operation room when persons' movement frequency was accumulated counted to 60. Conclusions During operation, persons' movement frequency will effect quantum of bacteria in air in laminar flow operation room directly,so we must strictly limit the number of persons' moving in or out operation room.%目的 了解并评价层流手术室中人员流动对空气含菌量的影响.方法 采用平板暴露法对20例手术进行术中空气采样,采样时间从层流30 min后手术患者入室前开始至手术结束,每隔30 min采样计数空气细菌;同时记录各时间段内人员流动次数.结果 层流手术室中各时间段平均人员流动次数及空气菌落数的相关系数为0.945,空气细菌含量与人员流动具有相关性,术中人员流动累计达60人次时空气微生物超过国家规定的普通手术室空气静态标准.结论 术中人员流动的次数,直接影响层流手术室空气中的细菌含量,层流手术室术中必须严格限制入室人员.
Daumer, M; Goldstein, S; Zanghì, N; Daumer, Martin; Durr, Detlef; Goldstein, Sheldon; Zangh, Nino
1996-01-01
A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about ``measuring operators'' that occurs when the subject is quantum mechanics. Without a specification of what should be meant by ``measuring'' a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Sch\\"rodinger's equation for a system of particles when we merely insist that ``particles'' means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm---for example, that we must a...
Li, Shu-Shen; Long, Gui-lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization.
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The rotational invariance under the usual physical angular momentum of the SUq(2) Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided. In addition, a new Hamiltonian for rotational spectra is introduced, based on the construction of irreducible tensor operators (ITOs) under SUq(2) and use of q-deformed tensor products and q-deformed Clebsch-Gordan coefficients. The rotational invariance of this SUq(2) ITO Hamiltonian under the usual physical angular momentum is explicitly proved and a simple closed expression for its energy spectrum (the ``hyperbolic tangent formula'') is introduced. Numerical tests against an experimental rotational band of HF are provided.
Directory of Open Access Journals (Sweden)
Ezzat G. Bakhoum
2015-01-01
Full Text Available This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need of supplementary support functions. Correlations with Lorentz transformation of wave functions by interaction with a certain material medium (the space-time origin of a wave-train being adjusted are also presented, and supplementary aspects regarding the use of electromagnetic scalar and vector potentials for modelling evolution within this alternating representation are added.
Raginsky, M
2003-01-01
We formulate and study, in general terms, the problem of quantum system identification, i.e., the determination (or estimation) of unknown quantum channels through their action on suitably chosen input density operators. We also present a quantitative analysis of the worst-case performance of these schemes.
Quantum robots plus environments.
Energy Technology Data Exchange (ETDEWEB)
Benioff, P.
1998-07-23
A quantum robot is a mobile quantum system, including an on board quantum computer and needed ancillary systems, that interacts with an environment of quantum systems. Quantum robots carry out tasks whose goals include making specified changes in the state of the environment or carrying out measurements on the environment. The environments considered so far, oracles, data bases, and quantum registers, are seen to be special cases of environments considered here. It is also seen that a quantum robot should include a quantum computer and cannot be simply a multistate head. A model of quantum robots and their interactions is discussed in which each task, as a sequence of alternating computation and action phases,is described by a unitary single time step operator T {approx} T{sub a} + T{sub c} (discrete space and time are assumed). The overall system dynamics is described as a sum over paths of completed computation (T{sub c}) and action (T{sub a}) phases. A simple example of a task, measuring the distance between the quantum robot and a particle on a 1D lattice with quantum phase path dispersion present, is analyzed. A decision diagram for the task is presented and analyzed.
Quantum stochastic calculus associated with quadratic quantum noises
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, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Quantum cryptography in free space.
Jacobs, B C; Franson, J D
1996-11-15
The range of quantum cryptography systems using optical fibers is limited to roughly 30 km because amplifiers cannot be used. A fully operational system for quantum cryptography based on the transmission of single photons in free space under daylight conditions has been demonstrated. The feasibility of a global system for quantum cryptography based on a network of ground stations and satellites is discussed.
Zyskin, M
1995-01-01
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field O(k) and the regularization .
Quantum State Tomography Based on Quantum Games Theoretic Setup
Nawaz, Ahmad
2009-01-01
We develop a technique for single qubit quantum state tomography using the mathematical setup of generalized quantization scheme for games. In our technique Alice sends an unknown pure quantum state to Bob who appends it with |0><0| and then applies the unitary operators on the appended quantum state and finds the payoffs for Alice and himself. It is shown that for a particular set of unitary operators these elements become equal to Stokes parameters for an unknown quantum state. In this way an unknown quantum state can be measured and reconstructed. Strictly speaking this technique is not a game as no strategic competitions are involved.
Unknown Quantum States The Quantum de Finetti Representation
Caves, C M; Schack, R; Caves, Carlton M.; Fuchs, Christopher A.; Schack, Ruediger
2002-01-01
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an ``unknown quantum state'' in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than...
Quantum Distinction: Quantum Distinctiones!
Zeps, Dainis
2009-01-01
10 pages; How many distinctions, in Latin, quantum distinctiones. We suggest approach of anthropic principle based on anthropic reference system which should be applied equally both in theoretical physics and in mathematics. We come to principle that within reference system of life subject of mathematics (that of thinking) should be equated with subject of physics (that of nature). For this reason we enter notions of series of distinctions, quantum distinction, and argue that quantum distinct...
Resolution of quantum singularities
Konkowski, Deborah; Helliwell, Thomas
2017-01-01
A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.
Gerry, Christopher; Knight, Peter
2004-10-01
1. Introduction; 2. Field quantization; 3. Coherent states; 4. Emission and absorption of radiation by atoms; 5. Quantum coherence functions; 6. Beam splitters and interferometers; 7. Nonclassical light; 8. Dissipative interactions and decoherence; 9. Optical test of quantum mechanics; 10. Experiments in cavity QED and with trapped ions; 11. Applications of entanglement: Heisenberg-limited interferometry and quantum information processing; Appendix A. The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy; Appendix B. Quantum measurement theory in a (very small) nutshell; Appendix C. Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions; Appendix D. Nonlinear optics and spontaneous parametric down-conversion.
Avoiding Quantum Chaos in Quantum Computation
Berman, G P; Izrailev, F M; Tsifrinovich, V I
2001-01-01
We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting
Scheme of thinking quantum systems
Yukalov, V I
2009-01-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Scheme of thinking quantum systems
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Termination of Nondeterministic Quantum Programs
Li, Yangjia; Ying, Mingsheng
2012-01-01
We define a language-independent model of nondeterministic quantum programs in which a quantum program consists of a finite set of quantum processes. These processes are represented by quantum Markov chains over the common state space. An execution of a nondeterministic quantum program is modeled by a sequence of actions of individual processes. These actions are described by super-operators on the state Hilbert space. At each step of an execution, a process is chosen nondeterministically to perform the next action. A characterization of reachable space and a characterization of diverging states of a nondeterministic quantum program are presented. We establish a zero-one law for termination probability of the states in the reachable space of a nondeterministic quantum program. A combination of these results leads to a necessary and sufficient condition for termination of nondeterministic quantum programs. Based on this condition, an algorithm is found for checking termination of nondeterministic quantum progr...
Duality Computing in Quantum Computers
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang
2008-01-01
In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.
Fluctuations in quantum devices
Directory of Open Access Journals (Sweden)
H.Haken
2004-01-01
Full Text Available Logical gates can be formalized by Boolean algebra whose elementary operations can be realized by devices that employ the interactions of macroscopic numbers of elementary excitations such as electrons, holes, photons etc. With increasing miniaturization to the nano scale and below, quantum fluctuations become important and can no longer be ignored. Based on Heisenberg equations of motion for the creation and annihilation operators of elementary excitations, I determine the noise sources of composite quantum systems.
Quantum Cryptography in Practice
Elliott, C; Troxel, G; Elliott, Chip; Pearson, David; Troxel, Gregory
2003-01-01
BBN, Harvard, and Boston University are building the DARPA Quantum Network, the world's first network that delivers end-to-end network security via high-speed Quantum Key Distribution, and testing that Network against sophisticated eavesdropping attacks. The first network link has been up and steadily operational in our laboratory since December 2002. It provides a Virtual Private Network between private enclaves, with user traffic protected by a weak-coherent implementation of quantum cryptography. This prototype is suitable for deployment in metro-size areas via standard telecom (dark) fiber. In this paper, we introduce quantum cryptography, discuss its relation to modern secure networks, and describe its unusual physical layer, its specialized quantum cryptographic protocol suite (quite interesting in its own right), and our extensions to IPsec to integrate it with quantum cryptography.
Goswami, Debashish
2016-01-01
This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitl...
Reversible quantum cellular automata
Schumacher, B
2004-01-01
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules generating such automata. The same local rules also generate the global time step for automata with periodic boundary conditions. Our main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme. This implies that, in contrast to the classical case, the inverse of a nearest neighbor quantum cellular automaton is again a nearest neighbor automaton. We present several construction methods for quantum cellular automata, based on unitaries commuting with their translates, on the quantization of (arbitrary) reversible classical cellular automata, on quantum c...
A quantum computer on the basis of an atomic quantum transistor with built-in quantum memory
Moiseev, S. A.; Andrianov, S. N.
2016-12-01
A quantum transistor based quantum computer where the multiqubit quantum memory is a component of the quantum transistor and, correspondingly, takes part in the performance of quantum logical operations is considered. Proceeding from the generalized Jaynes-Cummings model, equations for coefficients of the wave function of the quantum system under consideration have been obtained for different stages of its evolution in processes of performing logical operations. The solution of the system of equations allows one to establish requirements that are imposed on the parameters of the initial Hamiltonian and must be satisfied for the effective operation of the computer; it also demonstrates the possibility of a universal set of quantum operations. Thus, based on the proposed approach, the possibility of constructing a compact multiatomic ensemble based on quantum computer using a quantum transistor for the implementation of two-qubit gates has been demonstrated.
Quantum Computational Cryptography
Kawachi, Akinori; Koshiba, Takeshi
As computational approaches to classical cryptography have succeeded in the establishment of the foundation of the network security, computational approaches even to quantum cryptography are promising, since quantum computational cryptography could offer richer applications than the quantum key distribution. Our project focused especially on the quantum one-wayness and quantum public-key cryptosystems. The one-wayness of functions (or permutations) is one of the most important notions in computational cryptography. First, we give an algorithmic characterization of quantum one-way permutations. In other words, we show a necessary and sufficient condition for quantum one-way permutations in terms of reflection operators. Second, we introduce a problem of distinguishing between two quantum states as a new underlying problem that is harder to solve than the graph automorphism problem. The new problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. We show that the problem has several cryptographic properties and they enable us to construct a quantum publickey cryptosystem, which is likely to withstand any attack of a quantum adversary.
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, C.S. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
Canonical Quantum Teleportation of Two-Particle Arbitrary State
Institute of Scientific and Technical Information of China (English)
HAO Xiang; ZHU Shi-Qun
2005-01-01
The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.
Continuous history variable for programmable quantum processors
Vlasov, Alexander Yu
2010-01-01
In this brief note is discussed application of continuous quantum history ("trash") variable for simplification of scheme of programmable quantum processor. Similar scheme may be tested also in other models of the theory of quantum algorithms and complexity, because provides modification of a standard operation: quantum function evaluation.
Quantum Teichm\\"uller space from quantum plane
Frenkel, Igor B
2010-01-01
We derive the quantum Teichm\\"uller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum mutation operator arises from the tensor cube, the pentagon identity from the tensor fourth power of the canonical representation, and an operator of order three from isomorphisms between canonical representation and its left and right duals. We also show that the quantum universal Teichm\\"uller space is realized in the infinite tensor power of the canonical representation naturally indexed by rational numbers including the infinity. This suggests a relation to the same index set in the classification of projective modules over the quantum torus, the unitary counterpart of the quantum plane, and points to a new quantization of the universal Teichm\\"uller space.
Yamashita, Taro; Miki, Shigehito; Terai, Hirotaka; Makise, Kazumasa; Wang, Zhen
2012-07-15
We demonstrate the successful operation of a multielement superconducting nanowire single-photon detector (SSPD) array integrated with a single-flux-quantum (SFQ) readout circuit in a compact 0.1 W Gifford-McMahon cryocooler. A time-resolved readout technique, where output signals from each element enter the SFQ readout circuit with finite time intervals, revealed crosstalk-free operation of the four-element SSPD array connected with the SFQ readout circuit. The timing jitter and the system detection efficiency were measured to be 50 ps and 11.4%, respectively, which were comparable to the performance of practical single-pixel SSPD systems.
Steane, A M
1998-01-01
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, the review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the EPR experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory, and, arguably, quantum from classical physics. Basic quantum information ideas are described, including key distribution, teleportation, data compression, quantum error correction, the universal quantum computer and qua...
Emergent quantum mechanics and emergent symmetries
Hooft, G. 't
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such
Secure quantum network coding for controlled repeater networks
Shang, Tao; Li, Jiao; Liu, Jian-wei
2016-07-01
To realize efficient quantum communication based on quantum repeater, we propose a secure quantum network coding scheme for controlled repeater networks, which adds a controller as a trusted party and is able to control the process of EPR-pair distribution. As the key operations of quantum repeater, local operations and quantum communication are designed to adopt quantum one-time pad to enhance the function of identity authentication instead of local operations and classical communication. Scheme analysis shows that the proposed scheme can defend against active attacks for quantum communication and realize long-distance quantum communication with minimal resource consumption.
Keyl, M.; Kiukas, J.; Werner, R. F.
2016-05-01
In this paper, we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them, in particular, with a number of different (but equivalent) families of seminorms which turns the space of Schwartz operators into a Fréchet space. The study of the topological dual leads to non-commutative tempered distributions which are discussed in detail as well. We show, in particular, that the latter can be identified with a certain class of quadratic forms, therefore making operations like products with bounded (and also some unbounded) operators and quantum harmonic analysis available to objects which are otherwise too singular for being a Hilbert space operator. Finally, we show how the new methods can be applied by studying operator moment problems and convergence properties of fluctuation operators.
Gosson, Maurice A. de
2012-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level set...
Recoverability in quantum information theory
Wilde, Mark M
2015-01-01
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information...
Fault-tolerant quantum computation
Preskill, J
1997-01-01
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.
Quantum Coherence as a Resource
Streltsov, Alexander; Plenio, Martin B
2016-01-01
The coherent superposition of states, in combination with energy quantization, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted a considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has only been initiated recently. In this Colloquium we discuss and review the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Quantum statistical testing of a quantum random number generator
Humble, Travis S.
2014-10-01
The unobservable elements in a quantum technology, e.g., the quantum state, complicate system verification against promised behavior. Using model-based system engineering, we present methods for verifying the operation of a prototypical quantum random number generator. We begin with the algorithmic design of the QRNG followed by the synthesis of its physical design requirements. We next discuss how quantum statistical testing can be used to verify device behavior as well as detect device bias. We conclude by highlighting how system design and verification methods must influence effort to certify future quantum technologies.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
Fresnel-Transform's Quantum Correspondence and Quantum Optical ABCD Law
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; HU Li-Yun
2007-01-01
@@ Corresponding to the Fresnel transform there exists a unitary operator in quantum optics theory, which could be known the Fresnel operator (FO). We show that the multiplication rule of the FO naturally leads to the quantum optical ABCD law. The canonical operator methods as mapping of ray-transfer ABCD matrix is explicitly shown by the normally ordered expansion of the FO through the coherent state representation and the technique of integration within an ordered product of operators. We show that time evolution of the damping oscillator embodies the quantum optical ABCD law.
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Structural complexity of quantum networks
Energy Technology Data Exchange (ETDEWEB)
Siomau, Michael [Physics Department, Jazan University, P.O.Box 114, 45142 Jazan (Saudi Arabia); Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany)
2016-06-10
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e. mutual position of nodes and channels connecting them. We show here that the classical structural complexity of a quantum network does not restrict the structural complexity of entanglement graphs, which may be created in the quantum network with local operations and classical communication. We show, in particular, that 1D quantum network can simulate both simple entanglement graphs such as lattices and random graphs and complex small-world graphs.
Quantum computing and the entanglement frontier
Preskill, John
2012-01-01
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly entangled quantum systems efficiently, and we hope to hasten the day when well controlled quantum systems can perform tasks surpassing what can be done in the classical world. One way to achieve such "quantum supremacy" would be to run an algorithm on a quantum computer which solves a problem with a super-polynomial speedup relative to classical computers, but there may be other ways that can be achieved sooner, such as simulating exotic quantum states of strongly correlated matter. To operate a large scale quantum computer reliably we will need to overcome the debilitating effects of decoherence, which might be done using "standard" quantum hardware protected by quantum error-correcting codes, or by exploiting the nonabelian quantum statistics of anyons realized in solid state sy...
Quantum computation with two-dimensional graphene quantum dots
Institute of Scientific and Technical Information of China (English)
Li Jie-Sen; Li Zhi-Bing; Yao Dao-Xin
2012-01-01
We study an array of graphene nano sheets that form a two-dimensional S =1/2 Kagome spin lattice used for quantum computation.The edge states of the graphene nano sheets axe used to form quantum dots to confine electrons and perform the computation.We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots.It is shown that both schemes contain a great amount of information for quantum computation.The corresponding gate operations are also proposed.
Biamonte, J D; Whitfield, J D; Fitzsimons, J; Aspuru-Guzik, A
2010-01-01
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be error resistant, easily controllable, and built using existing technology. Moving away from gate-model and projective measurement based implementations of quantum computing may offer a less resource-intensive, and consequently a more feasible solution. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-body interaction terms, using sparse Hamiltonians with at most three-body interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes...
Quantum independent increment processes
Franz, Uwe
2005-01-01
This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.
Quantum error correcting codes and one-way quantum computing: Towards a quantum memory
Schlingemann, D
2003-01-01
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding and decoding operations for stabilizer codes can be realized on a one-way quantum computer. This is based on the graph code representation for stabilizer codes, on the one hand, and the relation between cluster states and graph codes, on the other hand.
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
Gossip algorithms in quantum networks
Siomau, Michael
2017-01-01
Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip algorithms to quantum networks and show that any quantum network can be updated to optimal configuration with local operations and classical communication. This allows to speed-up - in the best case exponentially - the quantum information dissemination. Irrespective of the initial configuration of the quantum network, the update requiters at most polynomial number of local operations and classical communication.
Quantum mechanics for mathematicians
Takhtajan, Leon A
2008-01-01
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks ...
Elliott, C
2004-01-01
A team from BBN Technologies, Boston University, and Harvard University has recently built and begun to operate the world's first Quantum Key Distribution (QKD)network under DARPA sponsorship. The DARPA Quantum Network became fully operational on October 23, 2003 in BBN's laboratories, and in June 2004 was fielded through dark fiber under the streets of Cambridge, Mass., to link our campuses with non-stop quantum cryptography, twenty-four hours per day. As of December 2004, it consists of six nodes. Four are 5 MHz, BBN-built BB84 systems designed for telecommunications fiber and inter-connected by a photonic switch. Two are the electronics subsystems for a high speed free-space system designed and built by NIST. This paper describes the motivation for our work, the current status of the DARPA Quantum Network, its unique optical switching and key relay protocols, and our future plans.
Gupta, S; Gupta, Sanjay
2002-01-01
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\\log^k n), k\\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called \\emph{Quantum Neural Networks (QNNs)} is defined, building on Deutsch's model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schr\\"{o}dinger's equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural network...
Quantum Endpoint Detection Based on QRDA
Wang, Jian; Wang, Han; Song, Yan
2017-08-01
Speech recognition technology is widely used in many applications for man - machine interaction. To face more and more speech data, the computation of speech processing needs new approaches. The quantum computation is one of emerging computation technology and has been seen as useful computation model. So we focus on the basic operation of speech recognition processing, the voice activity detection, to present quantum endpoint detection algorithm. In order to achieve this algorithm, the n-bits quantum comparator circuit is given firstly. Then based on QRDA(Quantum Representation of Digital Audio), a quantum endpoint detection algorithm is presented. These quantum circuits could efficient process the audio data in quantum computer.
Quantum Endpoint Detection Based on QRDA
Wang, Jian; Wang, Han; Song, Yan
2017-10-01
Speech recognition technology is widely used in many applications for man - machine interaction. To face more and more speech data, the computation of speech processing needs new approaches. The quantum computation is one of emerging computation technology and has been seen as useful computation model. So we focus on the basic operation of speech recognition processing, the voice activity detection, to present quantum endpoint detection algorithm. In order to achieve this algorithm, the n-bits quantum comparator circuit is given firstly. Then based on QRDA(Quantum Representation of Digital Audio), a quantum endpoint detection algorithm is presented. These quantum circuits could efficient process the audio data in quantum computer.
Arrighi, Pablo
2016-01-01
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs---in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on Quantum Cellular Automata with another on Reversible Causal Graph Dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. Keywords: Quantum Lattice Gas Automata, Block-representation, Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum Graphity, Causal Dynamical Triangula...
Lodahl, Peter; Mahmoodian, Sahand; Stobbe, Søren; Rauschenbeutel, Arno; Schneeweiss, Philipp; Volz, Jürgen; Pichler, Hannes; Zoller, Peter
2017-01-25
Advanced photonic nanostructures are currently revolutionizing the optics and photonics that underpin applications ranging from light technology to quantum-information processing. The strong light confinement in these structures can lock the local polarization of the light to its propagation direction, leading to propagation-direction-dependent emission, scattering and absorption of photons by quantum emitters. The possibility of such a propagation-direction-dependent, or chiral, light-matter interaction is not accounted for in standard quantum optics and its recent discovery brought about the research field of chiral quantum optics. The latter offers fundamentally new functionalities and applications: it enables the assembly of non-reciprocal single-photon devices that can be operated in a quantum superposition of two or more of their operational states and the realization of deterministic spin-photon interfaces. Moreover, engineered directional photonic reservoirs could lead to the development of complex quantum networks that, for example, could simulate novel classes of quantum many-body systems.
Bonitz, Michael
2016-01-01
This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Entanglement and coherence in quantum state merging
Streltsov, A; Rana, S; Bera, M N; Winter, A; Lewenstein, M
2016-01-01
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging where two parties aim to merge their parts of a tripartite quantum state. In standard quantum state merging, entanglement is considered as an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process, and apply them to several relevant scenarios. While quantum state merging can lead to ...
Quantum secure direct communication and deterministic secure quantum communication
Institute of Scientific and Technical Information of China (English)
LONG Gui-lu; DENG Fu-guo; WANG Chuan; LI Xi-han; WEN Kai; WANG Wan-ying
2007-01-01
In this review article,we review the recent development of quantum secure direct communication(QSDC)and deterministic secure quantum communication(DSQC) which both are used to transmit secret message,including the criteria for QSDC,some interesting QSDC protocols,the DSQC protocols and QSDC network,etc.The difference between these two branches of quantum Communication is that DSOC requires the two parties exchange at least one bit of classical information for reading out the message in each qubit,and QSDC does not.They are attractivebecause they are deterministic,in particular,the QSDC protocol is fully quantum mechanical.With sophisticated quantum technology in the future,the QSDC may become more and more popular.For ensuring the safety of QSDC with single photons and quantum information sharing of single qubit in a noisy channel,a quantum privacy amplification protocol has been proposed.It involves very simple CHC operations and reduces the information leakage to a negligible small level.Moreover,with the one-party quantum error correction,a relation has been established between classical linear codes and quantum one-party codes,hence it is convenient to transfer many good classical error correction codes to the quantum world.The one-party quantum error correction codes are especially designed for quantum dense coding and related QSDC protocols based on dense coding.
de Gosson, Maurice A
2011-01-01
Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.
Wu, L A; Wu, Lian-Ao; Lidar, Daniel
2005-01-01
Quantum computation and communication offer unprecedented advantages compared to classical information processing. Currently, quantum communication is moving from laboratory prototypes into real-life applications. When quantum communication networks become more widespread it is likely that they will be subject to attacks by hackers, virus makers, and other malicious intruders. Here we introduce the concept of "quantum malware" to describe such human-made intrusions. We offer a simple solution for storage of quantum information in a manner which protects quantum networks from quantum malware.
Experimental Satellite Quantum Communications.
Vallone, Giuseppe; Bacco, Davide; Dequal, Daniele; Gaiarin, Simone; Luceri, Vincenza; Bianco, Giuseppe; Villoresi, Paolo
2015-07-24
Quantum communication (QC), namely, the faithful transmission of generic quantum states, is a key ingredient of quantum information science. Here we demonstrate QC with polarization encoding from space to ground by exploiting satellite corner cube retroreflectors as quantum transmitters in orbit and the Matera Laser Ranging Observatory of the Italian Space Agency in Matera, Italy, as a quantum receiver. The quantum bit error ratio (QBER) has been kept steadily low to a level suitable for several quantum information protocols, as the violation of Bell inequalities or quantum key distribution (QKD). Indeed, by taking data from different satellites, we demonstrate an average value of QBER=4.6% for a total link duration of 85 s. The mean photon number per pulse μ_{sat} leaving the satellites was estimated to be of the order of one. In addition, we propose a fully operational satellite QKD system by exploiting our communication scheme with orbiting retroreflectors equipped with a modulator, a very compact payload. Our scheme paves the way toward the implementation of a QC worldwide network leveraging existing receivers.