Maximally incompatible quantum observables
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Toigo, Alessandro, E-mail: alessandro.toigo@polimi.it [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy); Ziman, Mario, E-mail: ziman@savba.sk [RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava (Slovakia); Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno (Czech Republic)
2014-05-01
The existence of maximally incompatible quantum observables in the sense of a minimal joint measurability region is investigated. Employing the universal quantum cloning device it is argued that only infinite dimensional quantum systems can accommodate maximal incompatibility. It is then shown that two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible.
Yan-Gang Miao
2015-01-01
Full Text Available As a generalized uncertainty principle (GUP leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states—the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.
Zak, Michail
2008-01-01
A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).
Uncertainty under quantum measures and quantum memory
Xiao, Yunlong; Jing, Naihuan; Li-Jost, Xianqing
2017-04-01
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.
Principles of maximally classical and maximally realistic quantum mechanics
S M Roy
2002-08-01
Recently Auberson, Mahoux, Roy and Singh have proved a long standing conjecture of Roy and Singh: In 2-dimensional phase space, a maximally realistic quantum mechanics can have quantum probabilities of no more than + 1 complete commuting cets (CCS) of observables coexisting as marginals of one positive phase space density. Here I formulate a stationary principle which gives a nonperturbative deﬁnition of a maximally classical as well as maximally realistic phase space density. I show that the maximally classical trajectories are in fact exactly classical in the simple examples of coherent states and bound states of an oscillator and Gaussian free particle states. In contrast, it is known that the de Broglie–Bohm realistic theory gives highly nonclassical trajectories.
Beretta, G P
2001-01-01
In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, in this paper, together with a review of the general features of the nonlinear quantum (thermo)dynamics I proposed in a series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)], I show its exact equivalence with the maximal-entropy-production variational-principle formulation recently derived in S. Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on the formalism of general interest I developed for the analysis of composite systems, I show how the variational derivation can be extended to the case of a composite system to obtain the general form of my equation of motion, that turns out to be consistent with the demanding requirements of strong separability. Moreover, I propose a new intriguing fundamental ansat...
Quantum theory allows for absolute maximal contextuality
Amaral, Barbara; Cunha, Marcelo Terra; Cabello, Adán
2015-12-01
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number ϑ of the corresponding exclusivity graph are, respectively, the maximum of S for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which ϑ /α approaches n . Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.
Hobson, Art
2011-01-01
An earlier paper introduces quantum physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate…
Hobson, Art
2011-01-01
An earlier paper introduces quantum physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate…
Quantum Uncertainty and Fundamental Interactions
Tosto S.
2013-04-01
Full Text Available The paper proposes a simplified theoretical approach to infer some essential concepts on the fundamental interactions between charged particles and their relative strengths at comparable energies by exploiting the quantum uncertainty only. The worth of the present approach relies on the way of obtaining the results, rather than on the results themselves: concepts today acknowledged as fingerprints of the electroweak and strong interactions appear indeed rooted in the same theoretical frame including also the basic principles of special and general relativity along with the gravity force.
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
Where does quantum uncertainty come from?
Rozpędek, Filip; Kaniewski, Jedrzej; Coles, Patrick J.
2016-01-01
about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information, albeit a lack of quantum information. We...... to show that also for other measurements the amount of uncertainty is in part connected to a lack of information. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states....
Quantum preparation uncertainty and lack of information
Rozpędek, Filip; Kaniewski, Jędrzej; Coles, Patrick J.; Wehner, Stephanie
2017-02-01
The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. We answer this question affirmatively by showing that for the well known measurements employed in BB84 quantum key distribution (Bennett and Brassard 1984 Int. Conf. on Computer System and Signal Processing), the amount of uncertainty can indeed be related to the amount of available information about additional registers determining the choice of the measurement. We proceed to show that also for other measurements the amount of uncertainty is in part connected to a LOI. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states.
Measurement Uncertainty for Finite Quantum Observables
René Schwonnek
2016-06-01
Full Text Available Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method is semidefinite programming, which we apply to arbitrary finite collections of projective observables on a finite dimensional Hilbert space. The quantification of errors is based on an arbitrary cost function, which assigns a penalty to getting result x rather than y, for any pair ( x , y . This induces a notion of optimal transport cost for a pair of probability distributions, and we include an Appendix with a short summary of optimal transport theory as needed in our context. There are then different ways to form an overall figure of merit from the comparison of distributions. We consider three, which are related to different physical testing scenarios. The most thorough test compares the transport distances between the marginals of a joint measurement and the reference observables for every input state. Less demanding is a test just on the states for which a “true value” is known in the sense that the reference observable yields a definite outcome. Finally, we can measure a deviation as a single expectation value by comparing the two observables on the two parts of a maximally-entangled state. All three error quantities have the property that they vanish if and only if the tested observable is equal to the reference. The theory is illustrated with some characteristic examples.
Inconclusive quantum measurements and decisions under uncertainty
Yukalov, V I
2016-01-01
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a ge...
Generalized Uncertainty Principle and Analogue of Quantum Gravity in Optics
Braidotti, Maria Chiara; Conti, Claudio
2016-01-01
The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while implementing sub-wavelength optical schemes is how to overcome the limitations set by standard Fourier optics. A strategy to overcome these difficulties is to utilize the concept of generalized uncertainty principle (G-UP) that has been originally developed to study quantum gravity. In this paper we propose to use the concept of G-UP within the framework of optics to show that the generalized Schrodinger equation describing short pulses and ultra-focused beams predicts the existence of a minimal spatial or temporal scale which in turn implies the existence of maximally localized states. Using a Gaussian wavepacket with complex phase, we derive the corresponding generalized uncertainty relation and its maximally localized states. We numerically show that the presence of nonlin...
Octonionization of three player, two strategy maximally entangled quantum games
Ahmed, Aden; Bleiler, Steve; Khan, Faisal Shah
2008-01-01
We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then exploited to analyze and potentially classify the Nash equilibria in the quantum games.
Uncertainty relations and approximate quantum error correction
Renes, Joseph M.
2016-09-01
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.
Simple Resonance Hierarchy for Surmounting Quantum Uncertainty
Amoroso, Richard L.
2010-12-01
For a hundred years violation or surmounting the Quantum Uncertainty Principle has remained a Holy Grail of both theoretical and empirical physics. Utilizing an operationally completed form of Quantum Theory cast in a string theoretic Higher Dimensional (HD) form of Dirac covariant polarized vacuum with a complex Einstein energy dependent spacetime metric, M̂4±C4 with sufficient degrees of freedom to be causally free of the local quantum state, we present a simple empirical model for ontologically surmounting the phenomenology of uncertainty through a Sagnac Effect RF pulsed Laser Oscillated Vacuum Energy Resonance hierarchy cast within an extended form of a Wheeler-Feynman-Cramer Transactional Calabi-Yau mirror symmetric spacetime bachcloth.
Dark Energy from Quantum Uncertainty of Simultaneity
Luo, M J
2014-01-01
The observed acceleration expansion of the universe was thought attribute to a mysterious dark energy in the framework of the classical general relativity. The dark energy behaves very similar with a vacuum energy in quantum mechanics. However, once the quantum effects are seriously taken into account, it predicts a wrong order of the vacuum energy and leads to a severe fine-tuning, known as the cosmological constant problem. We abandon the standard interpretation that time is a global parameter in quantum mechanics, replace it by a quantum dynamical variable playing the role of an operational quantum clock system. In the framework of reinterpretation of time, we find that the synchronization of two quantum clocks distance apart can not be realized in all rigor at quantum level. Thus leading to an intrinsic quantum uncertainty of simultaneity between spatial interval, which implies a visional vacuum energy fluctuation and gives an observed dark energy density $\\rho_{de}=\\frac{6}{\\pi}L_{P}^{-2}L_{H}^{-2}$, whe...
Uncertainty relations based on skew information with quantum memory
Ma, ZhiHao; Chen, ZhiHua; Fei, Shao-Ming
2017-01-01
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum correlations and tight bounds of uncertainty has been presented.
Inconclusive quantum measurements and decisions under uncertainty
Vyacheslav I. Yukalov
2016-04-01
Full Text Available We give a mathematical definition for the notion of inconclusive quantum measurements.In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy withthe theory of quantum measurements, the inconclusive quantum measurements correspond,in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluationof the considered prospect, and of an attraction factor, characterizing irrational,subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example,we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.
Inconclusive quantum measurements and decisions under uncertainty
Yukalov, Vyacheslav; Sornette, Didier
2016-04-01
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.
Quantum randomness certified by the uncertainty principle
Vallone, Giuseppe; Marangon, Davide G.; Tomasin, Marco; Villoresi, Paolo
2014-11-01
We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.
Scaling of the local quantum uncertainty at quantum phase transitions
Coulamy, I.B.; Warnes, J.H.; Sarandy, M.S., E-mail: msarandy@if.uff.br; Saguia, A.
2016-04-29
We investigate the local quantum uncertainty (LQU) between a block of L qubits and one single qubit in a composite system of n qubits driven through a quantum phase transition (QPT). A first-order QPT is analytically considered through a Hamiltonian implementation of the quantum search. In the case of second-order QPTs, we consider the transverse-field Ising chain via a numerical analysis through density matrix renormalization group. For both cases, we compute the LQU for finite-sizes as a function of L and of the coupling parameter, analyzing its pronounced behavior at the QPT. - Highlights: • LQU is suitable for the analysis of block correlations. • LQU exhibits pronounced behavior at quantum phase transitions. • LQU exponentially saturates in the quantum search. • Concavity of LQU indicates criticality in the Ising chain.
Generalized uncertainty principle and analogue of quantum gravity in optics
Braidotti, Maria Chiara; Musslimani, Ziad H.; Conti, Claudio
2017-01-01
The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while implementing sub-wavelength optical schemes is how to overcome the limitations set by standard Fourier optics. A strategy to overcome these difficulties is to utilize the concept of a generalized uncertainty principle (G-UP) which has been originally developed to study quantum gravity. In this paper we propose to use the concept of G-UP within the framework of optics to show that the generalized Schrödinger equation describing short pulses and ultra-focused beams predicts the existence of a minimal spatial or temporal scale which in turn implies the existence of maximally localized states. Using a Gaussian wavepacket with complex phase, we derive the corresponding generalized uncertainty relation and its maximally localized states. Furthermore, we numerically show that the presence of nonlinearity helps the system to reach its maximal localization. Our results may trigger further theoretical and experimental tests for practical applications and analogues of fundamental physical theories.
Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator
Vieira, Rafael; Amorim, Edgard P. M.; Rigolin, Gustavo
2013-11-01
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system’s time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.
Fredriksson, Albin, E-mail: albin.fredriksson@raysearchlabs.com; Hårdemark, Björn [RaySearch Laboratories, Sveavägen 44, Stockholm SE-111 34 (Sweden); Forsgren, Anders [Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm SE-100 44 (Sweden)
2015-07-15
Purpose: This paper introduces a method that maximizes the probability of satisfying the clinical goals in intensity-modulated radiation therapy treatments subject to setup uncertainty. Methods: The authors perform robust optimization in which the clinical goals are constrained to be satisfied whenever the setup error falls within an uncertainty set. The shape of the uncertainty set is included as a variable in the optimization. The goal of the optimization is to modify the shape of the uncertainty set in order to maximize the probability that the setup error will fall within the modified set. Because the constraints enforce the clinical goals to be satisfied under all setup errors within the uncertainty set, this is equivalent to maximizing the probability of satisfying the clinical goals. This type of robust optimization is studied with respect to photon and proton therapy applied to a prostate case and compared to robust optimization using an a priori defined uncertainty set. Results: Slight reductions of the uncertainty sets resulted in plans that satisfied a larger number of clinical goals than optimization with respect to a priori defined uncertainty sets, both within the reduced uncertainty sets and within the a priori, nonreduced, uncertainty sets. For the prostate case, the plans taking reduced uncertainty sets into account satisfied 1.4 (photons) and 1.5 (protons) times as many clinical goals over the scenarios as the method taking a priori uncertainty sets into account. Conclusions: Reducing the uncertainty sets enabled the optimization to find better solutions with respect to the errors within the reduced as well as the nonreduced uncertainty sets and thereby achieve higher probability of satisfying the clinical goals. This shows that asking for a little less in the optimization sometimes leads to better overall plan quality.
Quantum mechanics and the principle of maximal variety
Smolin, Lee
2015-01-01
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coor...
Quantum Gravitational Uncertainty of Transverse Position
Hogan, Craig J
2007-01-01
It is argued that holographic bounds on the information content of spacetime might be directly measurable. A new holographic uncertainty principle is conjectured as a quantum property of nearly flat spacetime: The spatial wavefunction of a body at rest at position L relative to any observer has a width in directions transverse to L greater than Delta x_H=C(Ll_P)^{1/2}, where l_p denotes the Planck length and C is of the order of unity. It is shown that this angular uncertainty Delta theta > C (l_P/L)^{1/2} corresponds to the information loss and nonlocality that occur if 3D space has a holographic dual description in terms of Planck-scale waves on a 2D screen with encoding close to the diffraction limit, and agrees with covariant holographic entropy bounds on total number of degrees of freedom. It is estimated that this effect can be precisely tested by interferometers capable of transverse position measurements, such as the Laser Interferometer Space Antenna.
Quantum theory of the generalised uncertainty principle
Bruneton, Jean-Philippe; Larena, Julien
2017-04-01
We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.
Some applications of uncertainty relations in quantum information
Majumdar, A. S.; Pramanik, T.
2016-08-01
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the Einstein, Podolsky and Rosen (EPR) paradox. Entropic uncertainty relations (EURs) are used to reveal quantum steering for non-Gaussian continuous variable states. EURs for discrete variables are studied in the context of quantum memory where fine-graining yields the optimum lower bound of uncertainty. The fine-grained uncertainty relation is used to obtain connections between uncertainty and the nonlocality of retrieval games for bipartite and tripartite systems. The Robertson-Schrödinger (RS) uncertainty relation is applied for distinguishing pure and mixed states of discrete variables.
Quantum Uncertainty and Decision-Making in Game Theory
Asano, M.; Ohya, M.; Tanaka, Y.; Khrennikov, A.; Basieva, I.
2011-01-01
Recently a few authors pointed to a possibility to apply the mathematical formalism of quantum mechanics to cognitive psychology, in particular, to games of the Prisoners Dilemma (PD) type.6_18 In this paper, we discuss the problem of rationality in game theory and point out that the quantum uncertainty is similar to the uncertainty of knowledge, which a player feels subjectively in his decision-making.
Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States
Banerji, Anindya; Panigrahi, Prasanta. K.; Singh, Ravindra Pratap; Chowdhury, Saurav; Bandyopadhyay, Abir
2012-01-01
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. ...
Uncertainty Principle in Loop Quantum Cosmology by Moyal Formalism
Perlov, Leonid
2016-01-01
In this paper we derive the uncertainty principle for the Loop Quantum Cosmology homogeneous and isotropic FLWR model with the holonomy-flux algebra. In our derivation we use the Wigner-Moyal-Groenewold phase space formalism. The formalism uses the characteristic functions and the Wigner transform, which maps the quantum operators to the functions on the phase space. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the Quantum Mechanics. One can derive from it both the canonical and path integral QM as well as the uncertainty principle. In this paper we apply the phase-space formalism to the quantum cosmology holonomy-flux algebra in case of the homogeneous and isotropic space to obtain the Loop Quantum Cosmology uncertainty principle.
Automated quantum conductance calculations using maximally-localised Wannier functions
Shelley, Matthew; Mostofi, Arash A; Marzari, Nicola
2011-01-01
A robust, user-friendly, and automated method to determine quantum conductance in disordered quasi-one-dimensional systems is presented. The scheme relies upon an initial density- functional theory calculation in a specific geometry after which the ground-state eigenfunctions are transformed to a maximally-localised Wannier function (MLWF) basis. In this basis, our novel algorithms manipulate and partition the Hamiltonian for the calculation of coherent electronic transport properties within the Landauer-Buttiker formalism. Furthermore, we describe how short- ranged Hamiltonians in the MLWF basis can be combined to build model Hamiltonians of large (>10,000 atom) disordered systems without loss of accuracy. These automated algorithms have been implemented in the Wannier90 code[Mostofi et al, Comput. Phys. Commun. 178, 685 (2008)], which is interfaced to a number of electronic structure codes such as Quantum-ESPRESSO, AbInit, Wien2k, SIESTA and FLEUR. We apply our methods to an Al atomic chain with a Na defect...
Role of information theoretic uncertainty relations in quantum theory
Jizba, Petr, E-mail: p.jizba@fjfi.cvut.cz [FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1 (Czech Republic); ITP, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin (Germany); Dunningham, Jacob A., E-mail: J.Dunningham@sussex.ac.uk [Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH (United Kingdom); Joo, Jaewoo, E-mail: j.joo@surrey.ac.uk [Advanced Technology Institute and Department of Physics, University of Surrey, Guildford, GU2 7XH (United Kingdom)
2015-04-15
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
Minimal length uncertainty relation and gravitational quantum well
Brau, F.; Buisseret, F.
2006-01-01
The dynamics of a particle in a gravitational quantum well is studied in the context of nonrelativistic quantum mechanics with a particular deformation of a two-dimensional Heisenberg algebra. This deformation yields a new short-distance structure characterized by a finite minimal uncertainty in pos
Quantum coherence and uncertainty in the anisotropic XY chain
Karpat, G.; ćakmak, B.; Fanchini, F. F.
2014-09-01
We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in a transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second-order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of nonanalyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and we investigate the robustness of the factorization phenomenon at low temperatures.
Tsiliyannis, Christos Aristeides
2013-09-01
Hazardous waste incinerators (HWIs) differ substantially from thermal power facilities, since instead of maximizing energy production with the minimum amount of fuel, they aim at maximizing throughput. Variations in quantity or composition of received waste loads may significantly diminish HWI throughput (the decisive profit factor), from its nominal design value. A novel formulation of combustion balance is presented, based on linear operators, which isolates the wastefeed vector from the invariant combustion stoichiometry kernel. Explicit expressions for the throughput are obtained, in terms of incinerator temperature, fluegas heat recuperation ratio and design parameters, for an arbitrary number of wastes, based on fundamental principles (mass and enthalpy balances). The impact of waste variations, of recuperation ratio and of furnace temperature is explicitly determined. It is shown that in the presence of waste uncertainty, the throughput may be a decreasing or increasing function of incinerator temperature and recuperation ratio, depending on the sign of a dimensionless parameter related only to the uncertain wastes. The dimensionless parameter is proposed as a sharp a' priori waste 'fingerprint', determining the necessary increase or decrease of manipulated variables (recuperation ratio, excess air, auxiliary fuel feed rate, auxiliary air flow) in order to balance the HWI and maximize throughput under uncertainty in received wastes. A 10-step procedure is proposed for direct application subject to process capacity constraints. The results may be useful for efficient HWI operation and for preparing hazardous waste blends.
Spin and Uncertainty in the Interpretation of Quantum Mechanics.
Hestenes, David
1979-01-01
Points out that quantum mechanics interpretations, using Heisenberg's Uncertainty Relations for the position and momentum of an electron, have their drawbacks. The interpretations are limited to the Schrodinger theory and fail to take into account either spin or relativity. Shows why spin cannot be ignored. (Author/GA)
Pseudoharmonic oscillator in quantum mechanics with a generalized uncertainty principle
Boukhellout, Abdelmalek
2013-01-01
The pseudoharmonic oscillator potential is studied in quantum mechanics with a generalized uncertainty relation characterized by the existence of a minimal length. By using the perturbative approach of Brau, we compute the correction to the energy spectrum in the first order of the minimal length parameter {\\beta}. The effect of the minimal length on the vibration-rotation of diatomic molecules is discussed.
Maximal entanglement versus entropy for mixed quantum states
Wei, T C; Goldbart, P M; Kwiat, P G; Munro, W J; Verstraete, F; Wei, Tzu-Chieh; Nemoto, Kae; Goldbart, Paul M.; Kwiat, Paul G.; Munro, William J.; Verstraete, Frank
2003-01-01
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy.
Stimulating Uncertainty: Amplifying the Quantum Vacuum with Superconducting Circuits
Nation, P D; Blencowe, M P; Nori, Franco
2011-01-01
The ability to generate particles from the quantum vacuum is one of the most pro- found consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, may soon be able to realize the elusive verification of the dynamical Casimir effect and analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.
Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits
Nation, P. D.; Johansson, J. R.; Blencowe, M. P.; Nori, Franco
2012-01-01
The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg’s uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analog Hawking radiation. This Colloquium article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analog, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.
Uncertainty relations in quantum optics. Is the photon intelligent?
Przanowski, Maciej; García-Compeán, Hugo; Tosiek, Jaromir; Turrubiates, Francisco J.
2016-10-01
The Robertson-Schrödinger, Heisenberg-Robertson and Trifonov uncertainty relations for arbitrary two functions f1 and f2 depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties (Δf1) 2 ṡ(Δf2) 2 or the sum (Δf1) 2 +(Δf2) 2 are investigated for the cases f1 = ϕ , exp(iϕ) , exp(- iϕ) , cos ϕ , sin ϕ and f2 = n.
Quantum-memory-assisted entropic uncertainty relations under weak measurements
Li, Lei; Wang, Qing-Wen; Shen, Shu-Qian; Li, Ming
2017-08-01
We investigate quantum-memory-assisted entropic uncertainty relations (EURs) based on weak measurements. It is shown that the lower bound of EUR revealed by weak measurements is always larger than that revealed by the corresponding projective measurements. A series of lower bounds of EUR under both weak measurements and projective measurements are presented. Interestingly, the quantum-memory-assisted EUR based on weak measurements is a monotonically decreasing function of the strength parameter. Furthermore, some information-theoretic inequalities associated with weak measurements are also derived.
Quantum coherence and uncertainty in the anisotropic XY chain
2014-01-01
We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple exp...
Generation of Maximally Entangled Bell State in a Coupled Quantum Dot
ZHANG Ping; FAN Wen-Bin; DUAN Su-Qing; ZHAO Xian-Geng
2001-01-01
We show how the two interacting electrons in a field-driven coupled quantum dot can be used to prepare maximally entangled Bell states. The time durations of the oscillatory electric field for producing and maintaining such highly entangled states are identified by both analytic and exact numerical solutions of the quantum dynamical equations.
Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
Fan, Zheyong; Goertzel, Ben; Ren, Zhongzhou; Zeng, Huabi
2010-01-01
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.
Quadrature Uncertainty and Information Entropy of Quantum Elliptical Vortex States
Banerji, Anindya; Singh, Ravindra Pratap; Chowdhury, Saurav; Bandyopadhyay, Abir
2013-01-01
We study the quadrature uncertainty of the quantum elliptical vortex state using the associated Wigner function. Deviations from the minimum uncertainty states were observed due to the absence of the Gaussian nature. In our study of the entropy, we noticed that with increasing vorticity, entropy increases for both the modes. We further observed that, there exists an optimum value of ellipticity which gives rise to maximum entanglement of the two modes of the quantum elliptical vortex states. A further increase in ellipticity reduces the entropy thereby resulting in a loss of information carrying capacity. We check the validity of the entropic inequality relations, namely the subaddivity and the Araki-Lieb inequality. The later was satisfied only for a very small range of the ellipticity of the vortex while the former seemed to be valid at all values.
How Does Quantum Uncertainty Emerge from Deterministic Bohmian Mechanics?
Solé, A.; Oriols, X.; Marian, D.; Zanghì, N.
2016-10-01
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual positions of the particles and the wave function of the system; and the state of the system evolves deterministically. Thus, the Bohmian state can be compared with the state in classical mechanics, which is given by the positions and momenta of all the particles, and which also evolves deterministically. However, while in classical mechanics it is usually taken for granted and considered unproblematic that the state is, at least in principle, measurable, this is not the case in Bohmian mechanics. Due to the linearity of the quantum dynamical laws, one essential component of the Bohmian state, the wave function, is not directly measurable. Moreover, it turns out that the measurement of the other component of the state — the positions of the particles — must be mediated by the wave function; a fact that in turn implies that the positions of the particles, though measurable, are constrained by absolute uncertainty. This is the key to understanding how Bohmian mechanics, despite being deterministic, can account for all quantum predictions, including quantum randomness and uncertainty.
On the quantum mechanical solutions with minimal length uncertainty
Shababi, Homa; Pedram, Pouria; Chung, Won Sang
2016-06-01
In this paper, we study two generalized uncertainty principles (GUPs) including [X,P] = iℏ(1 + βP2j) and [X,P] = iℏ(1 + βP2 + kβ2P4) which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.
Lisi, A D; Illuminati, F; Vitali, D; Lisi, Antonio Di; Siena, Silvio De; Illuminati, Fabrizio; Vitali, David
2004-01-01
We introduce an efficient and robust scheme to generate maximally entangled states of two atomic ensembles. The scheme is based on quantum non-demolition measurements of total atomic populations and on quantum feedback conditioned by the measurements outputs. The high efficiency of the scheme is tested and confirmed numerically for photo-detection with ideal efficiency as well as in the presence of losses.
Yu, Min; Fang, Mao-Fa
2017-09-01
The dynamic properties of the quantum-memory-assisted entropic uncertainty relation for a system comprised of a qubit to be measured and a memory qubit are investigated. We explore the behaviors of the entropic uncertainty and its lower bound in three different cases: Only one of the two qubits interacts with an external environment and subjects to quantum-jump-based feedback control, or both of the two qubits independently experience their own environments and local quantum-jump-based feedback control. Our results reveal that the quantum-jump-based feedback control with an appropriate feedback parameter can reduce the entropic uncertainty and its lower bound, and for the three different scenarios, the reduction in the uncertainty relates to different physical quantities. Besides, we find out that the quantum-jump-based feedback control not only can remarkably decrease the entropic uncertainty, but also can make the uncertainty reach its lower bound where the dynamical map becomes unital.
Maximizing the information transfer in a quantum-limited light-scattering system
Lading, Lars; Jørgensen, Thomas Martini
1990-01-01
A quantum-limited light-scattering system is considered. The spatial configuration that maximizes a given figure of merit is investigated, assuming that the emitted light has Poisson photon statistics. A specific system for measuring the velocity of a small particle is considered as an example...
Reconsideration of the Uncertainty Relations and Quantum Measurements
Dumitru S.
2008-04-01
Full Text Available Discussions on uncertainty relations (UR and quantum measurements (QMS persisted until nowadays in publications about quantum mechanics (QM. They originate mainly from the conventional interpretation of UR (CIUR. In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and dis- cussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucial pieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i thought-experimental fictions or (ii sim- ple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an information- transmission model, in which the quantum observables are considered as random vari- ables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.
Reconsideration of the Uncertainty Relations and Quantum Measurements
Dumitru S.
2008-04-01
Full Text Available Discussions on uncertainty relations (UR and quantum measurements (QMS persisted until nowadays in publications about quantum mechanics (QM. They originate mainly from the conventional interpretation of UR (CIUR. In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and discussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucialpieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i thought-experimental fictions or (ii simple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an information-transmission model, in which the quantum observables are considered as random variables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.
MEI Yu-Xue; CHEN Lin; CHEN Yi-Xin
2006-01-01
@@ In a process of remote state preparation, the universality of quantum channel is an essential ingredient. That is, one quantum channel should be feasible to remotely prepare any given qubit state. This problem appears in a process where one uses non-maximally entangled state as the passage. We present a scheme in which any given qubit |φ〉 = cosθ|0〉 + sinθeiψ|1〉 could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled state with a high fidelity, under the condition that the receiver holds the knowledge of θ. This condition is helpful to reduce the necessary amount of quantum channels, which is proven to be a low quantity to realize the universality. We also give several methods to investigate the trade-off between this amount and the achievable fidelity of the protocol.
On the two new types of the higher order GUP with minimal length uncertainty and maximal momentum
Homa Shababi
2017-07-01
Full Text Available In this letter, we present two new types of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP which are predicted both a minimal length uncertainty and a maximal observable momentum. Then, using these GUPs, we study the density of states for D-dimensional spherical coordinate systems in the momentum space. Also, we investigate the cosmological constant in the presence of these GUPs and finally, compare their massless type with the ones were predicted by Kempf and Pedram in Refs. [1] and [18]. Moreover, using a more general form of the higher order GUP, once again we compare the massless cosmological constants.
Erol, Volkan; Ozaydin, Fatih; Altintas, Azmi Ali
2014-06-24
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families
Niekamp, Soenke
2012-04-20
This thesis is concerned with different characterizations of multi-particle quantum correlations and with entropic uncertainty relations. The effect of statistical errors on the detection of entanglement is investigated. First, general results on the statistical significance of entanglement witnesses are obtained. Then, using an error model for experiments with polarization-entangled photons, it is demonstrated that Bell inequalities with lower violation can have higher significance. The question for the best observables to discriminate between a state and the equivalence class of another state is addressed. Two measures for the discrimination strength of an observable are defined, and optimal families of observables are constructed for several examples. A property of stabilizer bases is shown which is a natural generalization of mutual unbiasedness. For sets of several dichotomic, pairwise anticommuting observables, uncertainty relations using different entropies are constructed in a systematic way. Exponential families provide a classification of states according to their correlations. In this classification scheme, a state is considered as k-correlated if it can be written as thermal state of a k-body Hamiltonian. Witness operators for the detection of higher-order interactions are constructed, and an algorithm for the computation of the nearest k-correlated state is developed.
Horizon Quantum Mechanics of Generalized Uncertainty Principle Black Holes
Manfredi, Luciano
2016-01-01
We study the Horizon Wavefunction (HWF) description of a generalized uncertainty principle inspired metric that admits sub-Planckian black holes, where the black hole mass $m$ is replaced by $M = m\\left( 1 + \\frac{\\beta}{2} \\frac{M_{\\rm Pl}^2}{m^2} \\right)$. Considering the case of a wave-packet shaped by a Gaussian distribution, we compute the HWF and the probability ${\\cal {P}}_{BH}$ that the source is a (quantum) black hole, i.e., that it lies within its horizon radius. The case $\\beta0$, where a minimum in ${\\cal {P}}_{BH}$ is encountered, thus meaning that every particle has some probability of decaying to a black hole. Furthermore, for sufficiently large $\\beta$ we find that every particle is a quantum black hole, in agreement with the intuitive effect of increasing $\\beta$, which creates larger $M$ and $R_{H}$ terms. This is likely due to a "dimensional reduction" feature of the model, where the black hole characteristics for sub-Planckian black holes mimic those in $(1+1)$-dimensions and the horizon s...
Janssens, Bas
2010-01-01
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in open systems and its absence in closed ones, we prove sharp, state-independent inequalities reflecting the Heisenberg principle, the necessity of decoherence and the impossibility of perfect joint measurement. These bounds are used to judge how far a particular measurement is removed from the optimal one. We do this for a qubit interacting with the quantized EM field, continually probed using homodyne detection. We calculate to which extent this joint measurement is optimal. We then propose a two-step strategy to determine the (possibly mixed) state of n identically prepared qubits, and prove that it is asymptotically optimal in a local minimax sense, using `Quantum Local Asymptotic Normality' for qubits. We propose a physical implementation of QLAN, based on interaction wi...
One-mode quantum-limited Gaussian channels have Gaussian maximizers
2016-01-01
We prove that Gaussian states saturate the p->q norms of the one-mode quantum-limited attenuator and amplifier. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new logarithmic Sobolev inequality. Our result extends to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb, Invent. Math. 102, 179 (1990)), stating that Gaussian operators saturate the p->q norms of Gaussian...
Guo, Yi; Jiang, John N; Tang, Choon Yik; Ramakumar, Rama G
2010-01-01
This paper addresses the problem of controlling a variable-speed wind turbine with a Doubly Fed Induction Generator (DFIG), modeled as an electromechanically-coupled nonlinear system with rotor voltages and blade pitch angle as its inputs, active and reactive powers as its outputs, and most of the aerodynamic and mechanical parameters as its uncertainties. Using a blend of linear and nonlinear control strategies (including feedback linearization, pole placement, uncertainty estimation, and gradient-based potential function minimization) as well as time-scale separation in the dynamics, we develop a controller that is capable of maximizing the active power in the Maximum Power Tracking (MPT) mode, regulating the active power in the Power Regulation (PR) mode, seamlessly switching between the two modes, and simultaneously adjusting the reactive power to achieve a desired power factor. The controller consists of four cascaded components, uses realistic feedback signals, and operates without knowledge of the C_p-...
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2012-01-01
We show that a possible violation of the Robertson-Schr\\"odinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates the Robertson-Schr\\"odinger uncertainty principle) is always a quantum state of an appropriate non-commutative extension of quantum mechanics. Conversely, all canonical non-commutative extensions of quantum mechanics display states that violate the Robertson-Schr\\"odinger uncertainty principle.
Position-momentum uncertainty relations in the presence of quantum memory
Furrer, Fabian; Berta, Mario; Tomamichel, Marco
2014-01-01
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear...... operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused....... As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states....
Measurement uncertainties in the quantum formalism: quasi-realities of individual systems
Hofmann, Holger F
2012-01-01
The evaluation of uncertainties in quantum measurements is problematic since the correct value of an observable between state preparation and measurement is experimentally inaccessible. In Ozawa's formulation of uncertainty relations for quantum measurements, the correct value of an observable is represented by the operator of that observable. Here, I consider the implications of this operator-based assignment of values to individual systems and discuss the relation with weak values and weak measurement statistics.
Quantum Noise, Bits and Jumps: Uncertainties, Decoherence, Trajectories and Filtering
Belavkin, V P
2001-01-01
It is shown that many dissipative phenomena of "old" quantum mechanics which appeared 100 years ago in the form of the statistics of quantum thermal noise and quantum spontaneous jumps, have never been explained by the "new" conservative quantum mechanics discovered 75 years ago by Heisenberg and Schroedinger. This led to numerous quantum paradoxes which are reconsidered in this paper. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators from the algebra of the actual observables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of past observables with the potential future. This rule, together with the self-compatibility of measurements insuring the consistency of histories, is called the nondemolition principle. The application of this causality condition in the form of the dynamical ...
On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2014-01-01
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\\'{e}nyi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson-Schr\\"{o}ding...
On the Maximal Dimension of a Completely Entangled Subspace for Finite Level Quantum Systems
K R Parthasarathy
2004-11-01
Let $\\mathcal{H}_i$ be a finite dimensional complex Hilbert space of dimension $d_i$ associated with a finite level quantum system $A_i$ for $i=1, 2,\\ldots,k$. A subspace $S\\subset\\mathcal{H} = \\mathcal{H}_{A_1 A_2\\ldots A_k} = \\mathcal{H}_1 \\otimes \\mathcal{H}_2 \\otimes\\cdots\\otimes \\mathcal{H}_k$ is said to be completely entangled if it has no non-zero product vector of the form $u_1 \\otimes u_2 \\otimes\\cdots\\otimes u_k$ with $u_i$ in $\\mathcal{H}_i$ for each . Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic algebraic geometry we prove that $$\\max\\limits_{S\\in\\mathcal{E}}\\dim S=d_1 d_2\\ldots d_k-(d_1+\\cdots +d_k)+k-1,$$ where $\\mathcal{E}$ is the collection of all completely entangled subspaces. When $\\mathcal{H}_1 = \\mathcal{H}_2$ and $k = 2$ an explicit orthonormal basis of a maximal completely entangled subspace of $\\mathcal{H}_1 \\otimes \\mathcal{H}_2$ is given. We also introduce a more delicate notion of a perfectly entangled subspace for a multipartite quantum system, construct an example using the theory of stabilizer quantum codes and pose a problem.
Maximization of Extractable Randomness in a Quantum Random-Number Generator
Haw, J. Y.; Assad, S. M.; Lance, A. M.; Ng, N. H. Y.; Sharma, V.; Lam, P. K.; Symul, T.
2015-05-01
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However, in realistic scenarios, the raw output of a quantum random-number generator is inevitably tainted by classical technical noise. The integrity of the device can be compromised if this noise is tampered with or even controlled by some malicious party. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information-independent randomness that is quantified by min-entropy conditioned on this classical noise. We present a method for maximizing the conditional min entropy of the number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mb i t /s )/MHz . The spectral response of the detection system shows the potential to deliver more than 70 Gbit /s of random numbers in our experimental setup.
Zhang, Yanliang; Fang, Maofa; Kang, Guodong; Zhou, Qingping
2015-08-01
We have investigated the dynamic features of the quantum-memory-assisted entropic uncertainty relation (QMA EUR) in the amplitude damping (AD) channel. The initial state of qubit system and quantum memory system shared between Alice and Bob is assumed as extended by Werner-like (EWL) state. To reduce the amount of entropic uncertainty of Pauli observables in this noisy channel, we presented a reduction scheme by means of weak measurements (WMs) and weak measurement reversals (WMRs) before and after the entangled system subjecting to the noisy channel. It is shown that the prior WM and poster WMR can effectively reduce quantity of entropic uncertainty, but the poster WM operation cannot played a positive role on reduction of quantity of entropic uncertainty. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.
Uncertainty in the Classroom--Teaching Quantum Physics
Johansson, K. E.; Milstead, D.
2008-01-01
The teaching of the Heisenberg uncertainty principle provides one of those rare moments when science appears to contradict everyday life experiences, sparking the curiosity of the interested student. Written at a level appropriate for an able high school student, this article provides ideas for introducing the uncertainty principle and showing how…
Quantum Fractals: From Heisenberg's Uncertainty to Barnsley's Fractality
Jadczyk, Arkadiusz
2014-07-01
This book brings together two concepts. The first is over a hundred years old -- the "quantum", while the second, "fractals", is newer, achieving popularity after the pioneering work of Benoit Mandelbrot. Both areas of research are expanding dramatically day by day. It is somewhat amazing that quantum theory, in spite of its age, is still a boiling mystery as we see in some quotes from recent publications addressed to non-expert readers:...
Zhao, Ying-Jie
2016-01-01
We have introduced an improved exponential GUP, derived the maximally localized states, calculated quantum corrections to the thermodynamic quantities of the Schwardzschild black hole in our previous work. In this paper we continue to investigate how the maximally localized states and thermodynamic quantities such as Hawking temperature, the entropy, the heat capacity, the evaporation rate, and the decay time change in the extreme case that the integer n in our GUP rises to infinity.
Minimum uncertainty states for the quantum group SU{sub q}(2) and quantum Wigner d-functions
Mann, A.; Parthasarathy, R. [Institute of Mathematical Sciences, Madras (India)
1996-01-21
Minimum uncertainty angular momentum states for the quantum group SU{sub q}(2) are constructed. They involve the eigenvalues of J{sub 1} which are q-numbers and the quantum group analogue of the Wigner d-functions for {theta}={pi}/2. The result is generalized for all values of {theta} and a formula for the quantum Wigner d-function is derived. The case of q=1 is discussed and compared with the well known results for the Wigner d-functions. (author)
The effects of different quantum feedback types on the tightness of the variance-based uncertainty
Zheng, Xiao; Zhang, Guo-Feng
2017-03-01
The effect of the quantum feedback on the tightness of the variance-based uncertainty, the possibility of using quantum feedback to prepare the state with a better tightness, and the relationship between the tightness of the uncertainty and the mixedness of the system are studied. It is found that the tightness of Schrodinger-Robertson uncertainty (SUR) relation has a strict liner relationship with the mixedness of the system. As for the Robertson uncertainty relation (RUR), we find that the tightness can be enhanced by tuning the feedback at the beginning of the evolution. In addition, we deduce that the tightness of RUR has an inverse relationship with the mixedness and the relationship turns into a strict linear one when the system reach the steady state.
Putz, Mihai V.
2010-01-01
Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function. PMID:21152325
Mihai V. Putz
2010-10-01
Full Text Available Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor √1-n2, in terms of magnitude n ε [0,1] of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function.
Linear phase-space representations of quantum mechanics with minimal uncertainty in position
Menge, Edmund [Univ. Mainz (Germany); Leschke, Hajo [Univ. Erlangen (Germany)
2010-07-01
Quantum mechanics with a non-zero uncertainty in position can be generated by a one-parameter generalisation of the canonical commutation relation of ordinary quantum mechanics. This generalisation may be, for example, used in ''Quantum Loop Gravity''. For such a quantum mechanics with non-zero uncertainty in position a class of linear phase-space representations is defined, covering the well known phase space representation of Weyl, Wigner and Moyal as a limiting case. Applying the Lie-Trotter formula, these representations lead to a transcription of the new Schroedinger-Semigroup as a sequence of finite-dimensional integrals. These integrals can be informally be interpreted as a phase-space path integral.
Quantum Equilibrium and the Origin of Absolute Uncertainty
Dürr, D; Zanghì, N; D\\"urr, Detlef; Goldstein, Sheldon; Zangh\\'i, Nino
1992-01-01
The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr\\"odinger's equation for a system of particles when we merely insist that ``particles'' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an {\\it appearance} of randomness emerges, precisely as described by the quantum formalism and given, for example, by ``$\\rho=|\\psis|^2$.'' A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the p...
Position-momentum uncertainty relations in the presence of quantum memory
Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp [Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Berta, Mario [Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125 (United States); Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, 8093 Zürich (Switzerland); Tomamichel, Marco [School of Physics, The University of Sydney, Sydney 2006 (Australia); Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore); Scholz, Volkher B. [Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, 8093 Zürich (Switzerland); Christandl, Matthias [Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, 8093 Zürich (Switzerland); Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen (Denmark)
2014-12-15
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.
Uncertainty quantification for quantum chemical models of complex reaction networks.
Proppe, Jonny; Husch, Tamara; Simm, Gregor N; Reiher, Markus
2016-12-22
For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.
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.
Tightening the entropic uncertainty bound in the presence of quantum memory
Adabi, F.; Salimi, S.; Haseli, S.
2016-06-01
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables cannot be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. M. Berta et al. [Nat. Phys. 6, 659 (2010), 10.1038/nphys1734] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on the Holevo quantity and mutual information. We conclude that our lower bound will be tightened with respect to that of Berta et al. when the accessible information about measurements outcomes is less than the mutual information about the joint state. Some examples have been investigated for which our lower bound is tighter than Berta et al.'s lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has been obtained, as well as an upper bound for the regularized distillable common randomness.
Cryptography from quantum uncertainty in the presence of quantum side information
Bouman, Niek Johannes
2012-01-01
The thesis starts with a high-level introduction into cryptography and quantum mechanics. Chapter 2 gives a theoretical foundation by introducing probability theory, information theory, functional analysis, quantum mechanics and quantum information theory. Chapter 3, 4 and 5 are editions of work
Cryptography from quantum uncertainty in the presence of quantum side information
Bouman, Niek Johannes
2012-01-01
The thesis starts with a high-level introduction into cryptography and quantum mechanics. Chapter 2 gives a theoretical foundation by introducing probability theory, information theory, functional analysis, quantum mechanics and quantum information theory. Chapter 3, 4 and 5 are editions of work pub
A New Quantum Proxy Multi-signature Scheme Using Maximally Entangled Seven-Qubit States
Cao, Hai-Jing; Zhang, Jia-Fu; Liu, Jian; Li, Zeng-You
2016-02-01
In this paper, we propose a new secure quantum proxy multi-signature scheme using seven-qubit entangled quantum state as quantum channels, which may have applications in e-payment system, e-government, e-business, etc. This scheme is based on controlled quantum teleportation. The scheme uses the physical characteristics of quantum mechanics to guarantee its anonymity, verifiability, traceability, unforgetability and undeniability.
Uncertainty Relations and Quantum Effects of Constraints in Chern-Simons Theory
Nakamura, M
2013-01-01
It is well known that Chern-Simons Theories are in the constrained systems and their total Hamiltonians become identically zero, because of their gauge invariance. While treating the constraints quantum mechanially, it will be expected taht there remain the quantum fluctuations due to the uncertainty principle. Using the projection operator method (POM) and the theory of dynamical constraints, such fluctuation terms are systematically derived in the case of Abelian Chern-Simons theory. It is shown that these terms produce the effective mass in the complex scalar fields coupled to the CS fields.
Le, Thinh Phuc; Scarani, Valerio
2011-01-01
We define a family of reference-frame-independent quantum cryptography protocols for arbitrary dimensional signals. The generalized entropic uncertainty relations [M. Tomamichel and R. Renner, Phys. Rev. Lett. 106, 110506 (2011)] are used for the first time to derive security bounds for protocols which use more than two measurements and combine the statistics in a non-linear parameter. This shows the power and versatility of this technique compared to the heavier, though usually tighter, conventional techniques.
The quantum moment how Planck, Bohr, Einstein, and Eisenberg taught us to love uncertainty
Crease, Robert P
2014-01-01
The discovery of the quantum—the idea, born in the early 1900s in a remote corner of physics, that energy comes in finite packets instead of infinitely divisible quantities—planted a rich set of metaphors in the popular imagination. Quantum imagery and language now bombard us like an endless stream of photons. Phrases such as multiverses, quantum leaps, alternate universes, the uncertainty principle, and Schrödinger's cat get reinvented continually in cartoons and movies, coffee mugs and T-shirts, and fiction and philosophy, reinterpreted by each new generation of artists and writers. Is a "quantum leap" big or small? How uncertain is the uncertainty principle? Is this barrage of quantum vocabulary pretentious and wacky, or a fundamental shift in the way we think? All the above, say Robert P. Crease and Alfred Scharff Goldhaber in this pathbreaking book. The authors—one a philosopher, the other a physicist—draw on their training and six years of co-teaching to dramatize the quantum’s rocky path f...
Uncertainty relation for mutual information
Schneeloch, James; Broadbent, Curtis J.; Howell, John C.
2014-12-01
We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting that the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.
Alrawashdeh, Lubna R; Cronin, Michael P; Woodward, Clifford E; Day, Anthony I; Wallace, Lynne
2016-07-01
The weaker emission typically seen for iridium(III) cyclometalated complexes in aqueous medium can be reversed via encapsulation in cucurbit[10]uril (Q[10]). The Q[10] cavity is shown to effectively maximize quantum yields for the complexes, compared to any other medium. This may provide significant advantages for a number of sensor applications. NMR studies show that the complexes are accommodated similarly within the host molecule, even with cationic substituents attached to the ppy ligands, indicating that the hydrophobic effect is the dominant driving force for binding. Cavity-encapsulated 1:1 host-guest species dominate the emission, but 1:2 species are also indicated, which also give some enhancement of intensity. Results demonstrate that the enhancement is due primarily to much lower rates of nonradiative decay but also suggest that the encapsulation can cause a change in character of the emitting state.
Collective Uncertainty Entanglement Test
Rudnicki, Łukasz; Życzkowski, Karol
2011-01-01
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.
Consistency restrictions on maximal electric-field strength in quantum field theory.
Gavrilov, S P; Gitman, D M
2008-09-26
Quantum field theory with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean-energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter eET2, one can see that the leading contributions to the energy are due to the creation of particles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreaction.
Development of Quantum Chemical Method to Calculate Half Maximal Inhibitory Concentration (IC50 ).
Bag, Arijit; Ghorai, Pradip Kr
2016-05-01
Till date theoretical calculation of the half maximal inhibitory concentration (IC50 ) of a compound is based on different Quantitative Structure Activity Relationship (QSAR) models which are empirical methods. By using the Cheng-Prusoff equation it may be possible to compute IC50 , but this will be computationally very expensive as it requires explicit calculation of binding free energy of an inhibitor with respective protein or enzyme. In this article, for the first time we report an ab initio method to compute IC50 of a compound based only on the inhibitor itself where the effect of the protein is reflected through a proportionality constant. By using basic enzyme inhibition kinetics and thermodynamic relations, we derive an expression of IC50 in terms of hydrophobicity, electric dipole moment (μ) and reactivity descriptor (ω) of an inhibitor. We implement this theory to compute IC50 of 15 HIV-1 capsid inhibitors and compared them with experimental results and available other QASR based empirical results. Calculated values using our method are in very good agreement with the experimental values compared to the values calculated using other methods.
Maximal Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
Brodsky, Stanley J.; /SLAC /YITP, Stony Brook /Durham U.; Shrock, Robert; /YITP, Stony Brook
2008-08-01
Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator {bar q}q evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU(N) gauge theory with a variable number N{sub f} of massless fermions.
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
Koloğlu, Murat
2016-01-01
We analyze the classical and quantum vacua of 2d $\\mathcal{N}=(8,8)$ supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group, describing the worldvolume interactions of $N$ parallel D1-branes with flat transverse directions $\\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \\pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\\mathcal{N}=(8,8)$ sigma model into $(\\mathbb{R}^8)^{D-1}/\\mathbb{S}_D$ when $D=\\gcd(M,N)>1$, and by a single massive vacuum when $D=1$, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with an additional $U(1)$ 2-form gauge field $B$ coming from the string theory Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations, labeled by the $\\mathbb{Z}$-valued generalized electric flux and an independent $\\mathbb{Z}_N$-valued 't Hooft flux...
Quantum theory of the Generalised Uncertainty Principle and the existence of a Minimal Length
Bruneton, Jean-Philippe
2016-01-01
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \\delta_{ij} + g(P^2) P_i P_j $ for any functions $f$. However, we restrict our study to the case of commuting $X$'s. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus, specifically on whether they exhibit a mi...
Measurable Maximal Energy and Minimal Time Interval
Dahab, Eiman Abou El
2014-01-01
The possibility of finding the measurable maximal energy and the minimal time interval is discussed in different quantum aspects. It is found that the linear generalized uncertainty principle (GUP) approach gives a non-physical result. Based on large scale Schwarzshild solution, the quadratic GUP approach is utilized. The calculations are performed at the shortest distance, at which the general relativity is assumed to be a good approximation for the quantum gravity and at larger distances, as well. It is found that both maximal energy and minimal time have the order of the Planck time. Then, the uncertainties in both quantities are accordingly bounded. Some physical insights are addressed. Also, the implications on the physics of early Universe and on quantized mass are outlined. The results are related to the existence of finite cosmological constant and minimum mass (mass quanta).
Li, Xi-Zeng; Su, Bao-Xia
1994-01-01
It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
Hasegawa, Taisuke
2016-11-07
We propose a novel molecular dynamics (MD) algorithm for approximately dealing with a nuclear quantum dynamics in a real-time MD simulation. We have found that real-time dynamics of the ensemble of classical particles acquires quantum nature by introducing a constant quantum mechanical uncertainty constraint on its classical dynamics. The constant uncertainty constraint is handled by the Lagrange multiplier method and implemented into a conventional MD algorithm. The resulting constant uncertainty molecular dynamics (CUMD) is applied to the calculation of quantum position autocorrelation functions on quartic and Morse potentials. The test calculations show that CUMD gives better performance than ring-polymer MD because of the inclusion of the quantum zero-point energy during real-time evolution as well as the quantum imaginary-time statistical effect stored in an initial condition. The CUMD approach will be a possible starting point for new real-time quantum dynamics simulation in condensed phase.
Hasegawa, Taisuke
2016-11-01
We propose a novel molecular dynamics (MD) algorithm for approximately dealing with a nuclear quantum dynamics in a real-time MD simulation. We have found that real-time dynamics of the ensemble of classical particles acquires quantum nature by introducing a constant quantum mechanical uncertainty constraint on its classical dynamics. The constant uncertainty constraint is handled by the Lagrange multiplier method and implemented into a conventional MD algorithm. The resulting constant uncertainty molecular dynamics (CUMD) is applied to the calculation of quantum position autocorrelation functions on quartic and Morse potentials. The test calculations show that CUMD gives better performance than ring-polymer MD because of the inclusion of the quantum zero-point energy during real-time evolution as well as the quantum imaginary-time statistical effect stored in an initial condition. The CUMD approach will be a possible starting point for new real-time quantum dynamics simulation in condensed phase.
Minimal length, maximal momentum and thermodynamics of black body radiation
Shababi, Homa
2013-01-01
In this paper we study thermodynamics of black body radiation in the presence of quantum gravitational effects through a Generalized Uncertainty Principle that admits both a minimal measurable length and a maximal momentum. We focus on quantum gravity induced modifications of thermodynamical quantities in this framework. Some important issues such as the generalized Planck distribution, Wien s law and Dulong Petit law are studied in this setup with details.
Al-Hashimi, M H
2012-01-01
We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seems to violate the Heisenberg uncertainty relation. We use this as a motivation to derive a generalized uncertainty relation valid for an arbitrarily shaped quantum dot with general perfectly reflecting walls in $d$ dimensions. In addition, a general uncertainty relation for non-Hermitean operators is derived and applied to the non-Hermitean momentum operator in a quantum dot. We also consider minimal uncertainty wave packets in this situation, and we prove that the spectrum depends monotonically on the self-adjoint extension parameter. In addition, we construct the most general boundary conditions for semiconductor heterostructures such as quantum dots, quantum wires, and quantum wells, which are characterized by a 4-parameter family of self-adjoint extensions. Finally, we consider p...
Dmitri Sokolovski
2016-09-01
Full Text Available Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible outcomes. The paths are shaped from the virtual paths of the system, and the corresponding probabilities are determined by the measuring devices employed. If the measurements are highly accurate, the virtual paths become “real”, and the mean values of a quantity (a functional are directly related to the frequencies with which the paths are traveled. If the measurements are highly inaccurate, the mean (weak values are expressed in terms of the relative probabilities’ amplitudes. For pre- and post-selected systems they are bound to take arbitrary values, depending on the chosen transition. This is a direct consequence of the uncertainty principle, which forbids one from distinguishing between interfering alternatives, while leaving the interference between them intact.
Hirota, O; Sohma, M; Li Ming Wei; Tang, Z L; Liao, C C
2002-01-01
In this report, we simulate practical feature of Yuen-Kim protocol for quantum key distribution with unconditional secure. In order to demonstrate them experimentally by intensity modulation/direct detection(IMDD) optical fiber communication system, we use simplified encoding scheme to guarantee security for key information(1 or 0). That is, pairwise M-ary intensity modulation scheme is employed. Furthermore, we give an experimental implementation of YK protocol based on IMDD. A proof of Bell's theorem without inequalities for two maximally entangled particles is proposed using the technique of quantum teleportation. It follows Hardy's arguments for a non-maximally entangled state with the help of two auxiliary particles without correlation. The present proof can be tested by measurements with 100% probability.
When the uncertainty principle goes up to 11 or how to explain quantum physics with heavy metal
Moriarty, Philip
2018-01-01
There are deep and fascinating links between heavy metal and quantum physics. No, there are. Really. While teaching at the University of Nottingham, physicist Philip Moriarty noticed something odd--a surprising number of his students were heavily into metal music. Colleagues, too: a Venn diagram of physicists and metal fans would show a shocking amount of overlap. What's more, it turns out that heavy metal music is uniquely well-suited to explaining quantum principles. In When the Uncertainty Principle Goes Up to Eleven, Moriarty explains the mysteries of the universe's inner workings via drum beats and feedback: You'll discover how the Heisenberg uncertainty principle comes into play with every chugging guitar riff, what wave interference has to do with Iron Maiden, and why metalheads in mosh pits behave just like molecules in a gas. If you're a metal fan trying to grasp the complexities of quantum physics, a quantum physicist baffled by heavy metal, or just someone who'd like to know how the fundamental sci...
Radożycki, Tomasz
2016-11-01
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
Evaluation of Uncertainty on the Stages of Business Cycle: Implementation of Quantum Principles
Anna Svirina
2014-08-01
Full Text Available The goal of the research is to propose implementation of quantum principles for evaluation of economic development on stages of business cycle, define the difference between traditional (deterministic and quantum approaches and to provide quantitative analysis based argumentation for use of quantum economic principles in evaluation of internal and external factors on the stages of business cycle. The object of the study is possibility and reliability of quantum economic principles implementation to evaluate economic system performance. The authors analyze existing approaches towards implementation of deterministic, probabilistic and quantum models for estimating internal and external factors on stages of business cycle, define the benchmark for shift from traditional economy models and principles to quantum principles, describe the stages of business cycle from the quantum economics point of view and provide quantitative analysis of deterministic and quantum models quality on the level of enterprise to prove efficiency and reliability of quantum principles based approach. Calculations and data processing were carried out using Microsoft Excel and SSPS Statistics software.
Japaridze, George
2015-01-01
I discuss an upper bound on the boost and the energy of elementary particles. The limit is derived utilizing the core principle of relativistic quantum mechanics stating that there is a lower limit for localization of an elementary quantum system and the suggestion that when the localization scale reaches the Planck length, elementary particles are removed from observables. The limit for the boost and energy, $M_{Planck}/m$ and $M_{Planck}c^{2}\\approx\\,8.6* 10^{27}$ eV, is defined in terms of fundamental constants and the mass of elementary particle and does not involve any dynamic scale. These bounds imply that the cosmic ray flux of any flavor may stretch up to energies of order $10^{18}$ GeV and will cut off at this value.
Optimal entropic uncertainty relation for successive measurements in quantum information theory
M D Srinivas
2003-06-01
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in the literature on the sum of entropic uncertainties of two observables which are measured on distinct but identically prepared ensembles of systems. In the case of a two-dimensional Hilbert space, the optimum bound for successive measurements of two-spin components, is seen to be strictly greater than the optimal bound for the case when they are measured on distinct ensembles, except when the spin components are mutually parallel or perpendicular.
Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics
Pedram, Pouria
2013-01-01
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to $\\hbar\\sqrt{\\beta}$ and a maximal momentum proportional to $1/\\sqrt{\\beta}$, where $\\beta$ is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound on the dimensionless GUP parameter.
Exact ultra cold neutrons' energy spectrum in gravitational quantum mechanics
Pedram, Pouria
2013-10-01
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to and a maximal momentum proportional to , where β is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on Nesvizhevsky's famous experiment, we obtain an upper bound on the dimensionless GUP parameter.
Brüstle, Thomas; Pérotin, Matthieu
2012-01-01
Maximal green sequences are particular sequences of quiver mutations which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. Our aim is to initiate a systematic study of these sequences from a combinatorial point of view. Interpreting maximal green sequences as paths in various natural posets arising in representation theory, we prove the finiteness of the number of maximal green sequences for cluster finite quivers, affine quivers and acyclic quivers with at most three vertices. We also give results concerning the possible numbers and lengths of these maximal green sequences. Finally we describe an algorithm for computing maximal green sequences for arbitrary valued quivers which we used to obtain numerous explicit examples that we present.
Feng, Z.W.; Zu, X.T. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Li, H.L. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China); Yang, S.Z. [China West Normal University, Physics and Space Science College, Nanchong (China)
2016-04-15
We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle (GUP). The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of the Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of the black hole approaches the order of Planck scale, it stops radiating and leads to a black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomena imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at the Large Hadron Collider (LHC), and the results demonstrate that the black hole cannot be produced in the recent LHC. (orig.)
Brendle, Joerg
2016-01-01
We show that, consistently, there can be maximal subtrees of P (omega) and P (omega) / fin of arbitrary regular uncountable size below the size of the continuum. We also show that there are no maximal subtrees of P (omega) / fin with countable levels. Our results answer several questions of Campero, Cancino, Hrusak, and Miranda.
Mao, Ting; Yu, Yang
2010-01-01
We numerically investigated the quantum-classical transition in rf-superconducting quantum interference device (SQUID) systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent lambda(m), exhibits nonmonotonic behavior as a function of the coupling strength D. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of lambda(m)/D. In addition, the scaling holds in SQUID systems to a relatively smaller variant Planck's over [symbol: see text], suggesting the universality for this scaling.
Exact ultra cold neutrons' energy spectrum in gravitational quantum mechanics
Pedram, Pouria [Islamic Azad University, Department of Physics, Science and Research Branch, Tehran (Iran, Islamic Republic of)
2013-10-15
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to {Dirac_h}{radical}({beta}) and a maximal momentum proportional to 1/{radical}({beta}), where {beta} is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on Nesvizhevsky's famous experiment, we obtain an upper bound on the dimensionless GUP parameter. (orig.)
K B Athreya
2009-09-01
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy $\\int fh_id_=_i$ for $i=1,2,\\ldots,\\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\\exp(\\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.
Are CEOs Expected Utility Maximizers?
John List; Charles Mason
2009-01-01
Are individuals expected utility maximizers? This question represents much more than academic curiosity. In a normative sense, at stake are the fundamental underpinnings of the bulk of the last half-century's models of choice under uncertainty. From a positive perspective, the ubiquitous use of benefit-cost analysis across government agencies renders the expected utility maximization paradigm literally the only game in town. In this study, we advance the literature by exploring CEO's preferen...
Gaussian maximally multipartite entangled states
Facchi, Paolo; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio
2009-01-01
We introduce the notion of maximally multipartite entangled states (MMES) in the context of Gaussian continuous variable quantum systems. These are bosonic multipartite states that are maximally entangled over all possible bipartitions of the system. By considering multimode Gaussian states with constrained energy, we show that perfect MMESs, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of MMESs and their frustration for n <= 7.
High-dimensional quantum cloning and applications to quantum hacking.
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W; Karimi, Ebrahim
2017-02-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
High-dimensional quantum cloning and applications to quantum hacking
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W.; Karimi, Ebrahim
2017-01-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography. PMID:28168219
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...
Heisenberg's uncertainty principle
Busch, Paul; Heinonen, Teiko; Lahti, Pekka
2007-01-01
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and...
Dynamics of hydrogen-like atom bounded by maximal acceleration
Friedman, Yaakov
2012-01-01
The existence of a maximal acceleration for massive objects was conjectured by Caianiello 30 years ago based on the Heisenberg uncertainty relations. Many consequences of this hypothesis have been studied, but until now, there has been no evidence that boundedness of the acceleration may lead to quantum behavior. In previous research, we predicted the existence of a universal maximal acceleration and developed a new dynamics for which all admissible solutions have an acceleration bounded by the maximal one. Based on W. K\\"{u}ndig's experiment, as reanalyzed by Kholmetskii et al, we estimated its value to be of the order $10^{19}m/s^2$. We present here a solution of our dynamical equation for a classical hydrogen-like atom and show that this dynamics leads to some aspects of quantum behavior. We show that the position of an electron in a hydrogen-like atom can be described only probabilistically. We also show that in this model, the notion of "center of mass" must be modified. This modification supports the no...
Li, Xi-Zeng; Su, Bao-Xia
1996-01-01
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.
Uncertainty relation in Schwarzschild spacetime
Feng, Jun; Zhang, Yao-Zhong; Gould, Mark D.; Fan, Heng
2015-04-01
We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit -log2 c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
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.
Assaraf, Roland; Domin, Dominik
2014-03-01
We study the efficiency of quantum Monte Carlo (QMC) methods in computing space localized ground state properties (properties which do not depend on distant degrees of freedom) as a function of the system size N. We prove that for the commonly used correlated sampling with reweighting method, the statistical fluctuations σ2(N) do not obey the locality property. σ2(N) grow at least linearly with N and with a slope that is related to the fluctuations of the reweighting factors. We provide numerical illustrations of these tendencies in the form of QMC calculations on linear chains of hydrogen atoms.
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.
王栋; 叶柳
2012-01-01
Two schemes are put forward to remotely implement the preparation of a class of three-qubit W states,which employ maximally entangled states and non-maximally entangled states as the quantum channels,respectively.In the course of the preparations,some local quantum operations including threequbit projective measurements and unitary transformations are required.The success probability and classical information cost were worked out canoncally.The result shows that both schemes can be faithfully achieved in a probabilistic manner.Furthermore,the properties of the presented schemes were disscussed and their experimental feasibility was evaluated.It is found that the success probability can be doubled if the prepared states belong to some special ensembles,and the schemes can be well implemented with the current technologies.%基于最大纠缠信道和非最大纠缠信道,提出了两个一类三量子比特W态的远程制备方案.在制备过程中,需要实施三量子比特的投影测量和一些幺正操作.计算了方案的成功几率和经典信息量消耗.结果显示,两个方案都能以一定几率高保真度地实现.此外,讨论了方案的特性并进行了可行性分析.结果表明,当被制备态属于一些特殊态时成功几率大大提高；方案也是切合目前的实验技术,具有可行性.
Task-oriented maximally entangled states
Agrawal, Pankaj; Pradhan, B, E-mail: agrawal@iopb.res.i, E-mail: bpradhan@iopb.res.i [Institute of Physics, Sachivalaya Marg, Bhubaneswar, Orissa 751 005 (India)
2010-06-11
We introduce the notion of a task-oriented maximally entangled state (TMES). This notion depends on the task for which a quantum state is used as the resource. TMESs are the states that can be used to carry out the task maximally. This concept may be more useful than that of a general maximally entangled state in the case of a multipartite system. We illustrate this idea by giving an operational definition of maximally entangled states on the basis of communication tasks of teleportation and superdense coding. We also give examples and a procedure to obtain such TMESs for n-qubit systems.
On Uncertainties in Successive Measurements
Distler, Jacques
2012-01-01
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on the uncertainty of B in the initial state. What is relevant for a subsequent measurement of B, however, is the uncertainty of B in the post-measurement state. We make some remarks on the latter problem, both in the case where A has a pure point spectrum and in the case where A has a continuous spectrum.
Maximal coherence in a generic basis
Yao, Yao; Dong, G. H.; Ge, Li; Li, Mo; Sun, C. P.
2016-12-01
Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework of a resource theory of quantum coherence proposed recently, a fiducial basis should be preselected for characterizing the quantum coherence in specific circumstances, namely, the quantum coherence is a basis-dependent quantity. Therefore, a natural question is raised: what are the maximum and minimum coherences contained in a certain quantum state with respect to a generic basis? While the minimum case is trivial, it is not so intuitive to verify in which basis the quantum coherence is maximal. Based on the coherence measure of relative entropy, we indicate the particular basis in which the quantum coherence is maximal for a given state, where the Fourier matrix (or more generally, complex Hadamard matrices) plays a critical role in determining the basis. Intriguingly, though we can prove that the basis associated with the Fourier matrix is a stationary point for optimizing the l1 norm of coherence, numerical simulation shows that it is not a global optimal choice.
Uncertainty, non-locality and Bell's inequality
Pati, A K
1998-01-01
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local observables then the statistical predictions of hidden variable theory is well respected in quantum world. We argue that the uncertainties play a key role in understanding the non-locality issues in quantum world. Thus we can not rule out the possibility that a local, realistic hidden variable theory with statistical uncertainties in the observables might reproduce all the results of quantum theory.
Profit maximization mitigates competition
Dierker, Egbert; Grodal, Birgit
1996-01-01
We consider oligopolistic markets in which the notion of shareholders' utility is well-defined and compare the Bertrand-Nash equilibria in case of utility maximization with those under the usual profit maximization hypothesis. Our main result states that profit maximization leads to less price...... competition than utility maximization. Since profit maximization tends to raise prices, it may be regarded as beneficial for the owners as a whole. Moreover, if profit maximization is a good proxy for utility maximization, then there is no need for a general equilibrium analysis that takes the distribution...... of profits among consumers fully into account and partial equilibrium analysis suffices...
Uncertainty relation in Schwarzschild spacetime
Jun Feng
2015-04-01
Full Text Available We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time–energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit −log2c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
Variance-based uncertainty relations
Huang, Yichen
2010-01-01
It is hard to overestimate the fundamental importance of uncertainty relations in quantum mechanics. In this work, I propose state-independent variance-based uncertainty relations for arbitrary observables in both finite and infinite dimensional spaces. We recover the Heisenberg uncertainty principle as a special case. By studying examples, we find that the lower bounds provided by our new uncertainty relations are optimal or near-optimal. I illustrate the uses of our new uncertainty relations by showing that they eliminate one common obstacle in a sequence of well-known works in entanglement detection, and thus make these works much easier to access in applications.
Robust utility maximization in a discontinuous filtration
Jeanblanc, Monique; Ngoupeyou, Armand
2012-01-01
We study a problem of utility maximization under model uncertainty with information including jumps. We prove first that the value process of the robust stochastic control problem is described by the solution of a quadratic-exponential backward stochastic differential equation with jumps. Then, we establish a dynamic maximum principle for the optimal control of the maximization problem. The characterization of the optimal model and the optimal control (consumption-investment) is given via a forward-backward system which generalizes the result of Duffie and Skiadas (1994) and El Karoui, Peng and Quenez (2001) in the case of maximization of recursive utilities including model with jumps.
Quantum Gravity Effects On Charged Micro Black Holes Thermodynamics
Abbasvandi, N; Radiman, Shahidan; Abdullah, W A T Wan
2016-01-01
The charged black hole thermodynamics is corrected in terms of the quantum gravity effects. Most of the quantum gravity theories support the idea that near the Planck scale, the standard Heisenberg uncertainty principle should be reformulated by the so-called Generalized Uncertainty Principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of the minimal length and maximal momentum as GUP type I and the minimal length, minimal momentum, and maximal momentum as GUP type II on thermodynamics of the charged TeV-scale black holes. We also generalized our study to the universe with the extra dimensions based on the ADD model. In this framework, the effect of the electrical charge on thermodynamics of the black hole and existence of the charged black hole remnants as a potential candidate for the dark matter particles are discussed.
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Gamma-Ray Telescope and Uncertainty Principle
Shivalingaswamy, T.; Kagali, B. A.
2012-01-01
Heisenberg's Uncertainty Principle is one of the important basic principles of quantum mechanics. In most of the books on quantum mechanics, this uncertainty principle is generally illustrated with the help of a gamma ray microscope, wherein neither the image formation criterion nor the lens properties are taken into account. Thus a better…
Bartley, David; Lidén, Göran
2008-08-01
The reporting of measurement uncertainty has recently undergone a major harmonization whereby characteristics of a measurement method obtained during establishment and application are combined componentwise. For example, the sometimes-pesky systematic error is included. A bias component of uncertainty can be often easily established as the uncertainty in the bias. However, beyond simply arriving at a value for uncertainty, meaning to this uncertainty if needed can sometimes be developed in terms of prediction confidence in uncertainty-based intervals covering what is to be measured. To this end, a link between concepts of accuracy and uncertainty is established through a simple yet accurate approximation to a random variable known as the non-central Student's t-distribution. Without a measureless and perpetual uncertainty, the drama of human life would be destroyed. Winston Churchill.
The Effects of Minimal Length, Maximal Momentum, and Minimal Momentum in Entropic Force
Zhong-Wen Feng
2016-01-01
Full Text Available The modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum, and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole are investigated. Then, according to Verlinde’s theory, the generalized uncertainty principle (GUP corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes but also to the Planck length and the dimensionless constants α0 and β0. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein’s field equation (EFE and the modified Friedmann equation.
The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force
Feng, Zhong-Wen; Li, Hui-Ling; Zu, Xiao-Tao
2016-01-01
In this paper, the modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole is investigated. Then, according to Verlinde's theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes, but also to the Planck length and the dimensionless constants \\alpha_0\\ and \\beta_0\\. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein's field equation (EFE) and the modified Friedmann equation.
Maximally entangled mixed states made easy
Aiello, A; Voigt, D; Woerdman, J P
2006-01-01
We show that, contrarily to a recent claim [M. Ziman and V. Bu\\v{z}ek, Phys. Rev. A. \\textbf{72}, 052325 (2005)], it is possible to achieve maximally entangled mixed states of two qubits from the singlet state via the action of local nonunital quantum channels. Moreover, we present a simple, feasible linear optical implementation of one of such channels.
Lindley, Dennis V
2013-01-01
Praise for the First Edition ""...a reference for everyone who is interested in knowing and handling uncertainty.""-Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made.
Generalized Uncertainty Principle and Angular Momentum
Bosso, Pasquale
2016-01-01
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the Hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems.
Quantum computing and probability.
Ferry, David K
2009-11-25
Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.
Maximal temperature in a simple thermodynamical system
Dai, De-Chang
2016-01-01
Temperature in a simple thermodynamical system is not limited from above. It is also widely believed that it does not make sense talking about temperatures higher than the Planck temperature in the absence of the full theory of quantum gravity. Here, we demonstrate that there exist a maximal achievable temperature in a system where particles obey the laws of quantum mechanics and classical gravity before we reach the realm of quantum gravity. Namely, if two particles with a given center of mass energy come at the distance shorter than the Schwarzschild diameter apart, according to classical gravity they will form a black hole. It is possible to calculate that a simple thermodynamical system will be dominated by black holes at a critical temperature which is about three times lower than the Planck temperature. That represents the maximal achievable temperature in a simple thermodynamical system.
Parker, Andrew M.; Wandi Bruine de Bruin; Baruch Fischhoff
2007-01-01
Our previous research suggests that people reporting a stronger desire to maximize obtain worse life outcomes (Bruine de Bruin et al., 2007). Here, we examine whether this finding may be explained by the decision-making styles of self-reported maximizers. Expanding on Schwartz et al. (2002), we find that self-reported maximizers are more likely to show problematic decision-making styles, as evidenced by self-reports of less behavioral coping, greater dependence on others when making decisions...
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Ming Yi WANG; Guo ZHAO
2005-01-01
A right R-module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R-homomorphism f : m → E can be extended to an R-homomorphism f' : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R-module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R-module over any left perfect right self-injective ring R is the injective hull of a projective submodule.
Andrew M. Parker
2007-12-01
Full Text Available Our previous research suggests that people reporting a stronger desire to maximize obtain worse life outcomes (Bruine de Bruin et al., 2007. Here, we examine whether this finding may be explained by the decision-making styles of self-reported maximizers. Expanding on Schwartz et al. (2002, we find that self-reported maximizers are more likely to show problematic decision-making styles, as evidenced by self-reports of less behavioral coping, greater dependence on others when making decisions, more avoidance of decision making, and greater tendency to experience regret. Contrary to predictions, self-reported maximizers were more likely to report spontaneous decision making. However, the relationship between self-reported maximizing and worse life outcomes is largely unaffected by controls for measures of other decision-making styles, decision-making competence, and demographic variables.
Entanglement and discord assisted entropic uncertainty relations under decoherence
Yao, ChunMei; Chen, ZhiHua; Ma, ZhiHao; Severini, Simone; Serafini, Alessio
2014-09-01
The uncertainty principle is a crucial aspect of quantum mechanics. It has been shown that quantum entanglement as well as more general notions of correlations, such as quantum discord, can relax or tighten the entropic uncertainty relation in the presence of an ancillary system. We explored the behaviour of entropic uncertainty relations for system of two qubits-one of which subjects to several forms of independent quantum noise, in both Markovian and non-Markovian regimes. The uncertainties and their lower bounds, identified by the entropic uncertainty relations, increase under independent local unital Markovian noisy channels, but they may decrease under non-unital channels. The behaviour of the uncertainties (and lower bounds) exhibit periodical oscillations due to correlation dynamics under independent non-Markovian reservoirs. In addition, we compare different entropic uncertainty relations in several special cases and find that discord-tightened entropic uncertainty relations offer in general a better estimate of the uncertainties in play.
Quantum Physics Without Quantum Philosophy
Dürr, Detlef; Zanghì, Nino
2013-01-01
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Constraint Propagation as Information Maximization
Abdallah, A Nait
2012-01-01
Dana Scott used the partial order among partial functions for his mathematical model of recursively defined functions. He interpreted the partial order as one of information content. In this paper we elaborate on Scott's suggestion of regarding computation as a process of information maximization by applying it to the solution of constraint satisfaction problems. Here the method of constraint propagation can be interpreted as decreasing uncertainty about the solution -- that is, as gain in information about the solution. As illustrative example we choose numerical constraint satisfaction problems to be solved by interval constraints. To facilitate this approach to constraint solving we formulate constraint satisfaction problems as formulas in predicate logic. This necessitates extending the usual semantics for predicate logic so that meaning is assigned not only to sentences but also to formulas with free variables.
Thermodynamic and relativistic uncertainty relations
Artamonov, A. A.; Plotnikov, E. M.
2017-01-01
Thermodynamic uncertainty relation (UR) was verified experimentally. The experiments have shown the validity of the quantum analogue of the zeroth law of stochastic thermodynamics in the form of the saturated Schrödinger UR. We have also proposed a new type of UR for the relativistic mechanics. These relations allow us to consider macroscopic phenomena within the limits of the ratio of the uncertainty relations for different physical quantities.
Maximally entangled states in pseudo-telepathy games
Mančinska, Laura
2015-01-01
A pseudo-telepathy game is a nonlocal game which can be won with probability one using some finite-dimensional quantum strategy but not using a classical one. Our central question is whether there exist two-party pseudo-telepathy games which cannot be won with probability one using a maximally entangled state. Towards answering this question, we develop conditions under which maximally entangled states suffice. In particular, we show that maximally entangled states suffice for weak projection...
Rudiger Bubner
1998-12-01
Full Text Available Even though the maxims' theory is not at thecenter of Kant's ethics, it is the unavoidable basis of the categoric imperative's formulation. Kant leanson the transmitted representations of modem moral theory. During the last decades, the notion of maxims has deserved more attention, due to the philosophy of language's debates on rules, and due to action theory's interest in this notion. I here by brietly expound my views in these discussions.
Lorentz invariance violation and generalized uncertainty principle
Tawfik, Abdel Nasser; Magdy, H.; Ali, A. Farag
2016-01-01
There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay Δ t comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, Δ t, and the relative change in the speed of muon neutrino Δ v in dependence on redshift z turn to be wrong, we utilize its main features to estimate Δ v. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, a that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.
Minimum uncertainty and squeezing in diffusion processes and stochastic quantization
Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe
1994-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
Liu, Baoding
2015-01-01
When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, c...
Uncertainty principle in larmor clock
QIAO Chuan; REN Zhong-Zhou
2011-01-01
It is well known that the spin operators of a quantum particle must obey uncertainty relations.We use the uncertainty principle to study the Larmor clock.To avoid breaking the uncertainty principle,Larmor time can be defined as the ratio of the phase difference between a spin-up particle and a spin-down particle to the corresponding Larmor frequency.The connection between the dwell time and the Larmor time has also been confirmed.Moreover,the results show that the behavior of the Larmor time depends on the height and width of the barrier.
Quantum physics without quantum philosophy
Duerr, Detlef [Muenchen Univ. (Germany). Mathematisches Inst.; Goldstein, Sheldon [Rutgers State Univ., Piscataway, NJ (United States). Dept. of Mathematics; Zanghi, Nino [Genova Univ. (Italy); Istituto Nazionale Fisica Nucleare, Genova (Italy)
2013-02-01
Integrates and comments on the authors' seminal papers in the field. Emphasizes the natural way in which quantum phenomena emerge from the Bohmian picture. Helps to answer many of the objections raised to Bohmian quantum mechanics. Useful overview and summary for newcomers and students. It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schroedinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Multi Class Active Learning by Uncertainty Sampling with Diversity Maximization
2014-11-13
number of labels are difficult to get, which require much human labour . Generally speaking, there are three types of approaches to relieve the tedious...algorithm is based on the binary classifier SVM, it may become less effective when the data are multi-class. Motivated by the state of the art of active
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
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
Strange, P.
2012-01-01
In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive…
Nguyen, Daniel Xuyen
This paper presents a model of trade that explains why firms wait to export and why many exporters fail. Firms face uncertain demands that are only realized after the firm enters the destination. The model retools the timing of uncertainty resolution found in productivity heterogeneity models...... in untested destinations. The option to forecast demands causes firms to delay exporting in order to gather more information about foreign demand. Third, since uncertainty is resolved after entry, many firms enter a destination and then exit after learning that they cannot profit. This prediction reconciles...
Hadjiivanov, Ludmil
2015-01-01
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schr\\"odinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classical interpretation. We reproduce here their later (1971) version, reviewing on the way the generalization (and mathematical derivation) of Heisenberg's uncertainty relations (due to Weyl and Schr\\"odinger) needed for the passage from EPR to Bell. We also provide an improved derivation of the quantum theoretic violation of Bell's inequalities. Soon after the experimental confirmation of the quantum entanglement (culminati...
The effect of quantum noise on the restricted quantum game
Cao Shuai; Fang Mao-Fa
2006-01-01
It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0＜ p≤0.422 (p is the quantum noise parameter), while two special Nash equilibria appear in the range of 0.422 ＜ p＜ 1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player's payoff and the reduction of the quantum player's payoff, but is helpful in forming two Nash equilibria.
Heydorn, Kaj; Anglov, Thomas
2002-01-01
Methods recommended by the International Standardization Organisation and Eurachem are not satisfactory for the correct estimation of calibration uncertainty. A novel approach is introduced and tested on actual calibration data for the determination of Pb by ICP-AES. The improved calibration unce...
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)
Uncertainty Relations and Possible Experience
Gregg Jaeger
2016-06-01
Full Text Available The uncertainty principle can be understood as a condition of joint indeterminacy of classes of properties in quantum theory. The mathematical expressions most closely associated with this principle have been the uncertainty relations, various inequalities exemplified by the well known expression regarding position and momentum introduced by Heisenberg. Here, recent work involving a new sort of “logical” indeterminacy principle and associated relations introduced by Pitowsky, expressable directly in terms of probabilities of outcomes of measurements of sharp quantum observables, is reviewed and its quantum nature is discussed. These novel relations are derivable from Boolean “conditions of possible experience” of the quantum realm and have been considered both as fundamentally logical and as fundamentally geometrical. This work focuses on the relationship of indeterminacy to the propositions regarding the values of discrete, sharp observables of quantum systems. Here, reasons for favoring each of these two positions are considered. Finally, with an eye toward future research related to indeterminacy relations, further novel approaches grounded in category theory and intended to capture and reconceptualize the complementarity characteristics of quantum propositions are discussed in relation to the former.
The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force
Feng, Zhongwen
2016-01-01
In this paper, we generalize the entropic force law via a phenomenological interpretation of a most general kind of generalized uncertainty principle, which contains a minimal length, a minimal momentum and a maximal momentum. We first study the quantum corrections to the thermodynamics of black hole. Then, inspired by Verlinde's theory, the modified thermodynamics leads to the GUP corrected entropic force. The result shows that the GUP corrected entropic force do not only related to the properties of the black holes, but also affected by the Planck length, the dimensionless constants \\(alpha_0\\) and \\(beta_0\\). Based on the GUP corrected entropic force, we also derive the modified Einstein's field equations and the modified Friedmann equations.
Janusz Brzozowski
2014-05-01
Full Text Available The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result: If L is a regular language of quotient complexity n and G is the subgroup of permutations in the transition semigroup T of the minimal DFA of L, then L is maximally atomic if and only if G is transitive on k-subsets of 1,...,n for 0 <= k <= n and T contains a transformation of rank n-1.
Andersen, Klaus Ejner
1985-01-01
Guinea pig maximization tests (GPMT) with chlorocresol were performed to ascertain whether the sensitization rate was affected by minor changes in the Freund's complete adjuvant (FCA) emulsion used. Three types of emulsion were evaluated: the oil phase was mixed with propylene glycol, saline with...... to the saline/oil emulsion. Placing of the challenge patches affected the response, as simultaneous chlorocresol challenge on the flank located 2 cm closer to the abdomen than the usual challenge site gave decreased reactions....
Cooperative Communications via Dual-Teleportation with Non-maximally Entanglement Measurements
毛云; 郭迎; 曾贵华
2012-01-01
We investigate a framework of the cooperative quantum teleportation （CQT） based on non-maximally entangled state basis （NB） measurements,instead of maximally entangled state basis （MB） measurements.It is implemented with two consecutive conventional （or direct） quantum telportations （DQT）,where unknown quantum states can be transmitted in a point-to-point fashion.The security is based on the quantum-mechanical impossibility of local unitary transformations between non-maximally entangled states.It shows that the CQT can enhance the successful transmissions by self-correcting the errors introduced in the dual-teleportations.
Maximally entangled state can be a mixed state
Li, Zong-Guo; Fei, Shao-Ming; Fan, Heng; Liu, W M
2009-01-01
We present mixed maximally entangled states in d\\otimes d' (d'\\geq 2d) spaces. This result is beyond the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states in $d\\otimes d$ systems, for example, they can be used as a resource for faithful teleportation, their local distinguishability property is also the same as the pure states case. On the other hand, one advantage of these mixed maximally entangled states is that the decoherence induced by certain noisy quantum channel does not destroy their entanglement. Thus one party of these mixed states can be sent through this channel to arbitrary distance while still keeping them as a valuable resource for quantum information processing. We also propose a scheme to prepare these states and confirm their advantage in NMR physical system.
Social group utility maximization
Gong, Xiaowen; Yang, Lei; Zhang, Junshan
2014-01-01
This SpringerBrief explains how to leverage mobile users' social relationships to improve the interactions of mobile devices in mobile networks. It develops a social group utility maximization (SGUM) framework that captures diverse social ties of mobile users and diverse physical coupling of mobile devices. Key topics include random access control, power control, spectrum access, and location privacy.This brief also investigates SGUM-based power control game and random access control game, for which it establishes the socially-aware Nash equilibrium (SNE). It then examines the critical SGUM-b
Brandes, U; Gaertler, M; Goerke, R; Hoefer, M; Nikoloski, Z; Wagner, D
2006-01-01
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances.
Review on Generalized Uncertainty Principle
Tawfik, Abdel Nasser
2015-01-01
Based on string theory, black hole physics, doubly special relativity and some "thought" experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified dispersion relation, the space noncommutativity, the Lorentz invariance violation, and the quantum-gravity-induced birefringence effects are summarized. The origin of minimal measurable quantities and the different GUP approaches are reviewed and the corresponding observations are analysed. Bounds on the GUP parameter are discussed and implemented in understanding recent PLANCK observations on the cosmic inflation. The higher-order GUP approaches predict minimal length uncertainty with and without maximum momenta.
Maximizing without difficulty: A modified maximizing scale and its correlates
Linda Lai
2010-01-01
This article presents several studies that replicate and extend previous research on maximizing. A modified scale for measuring individual maximizing tendency is introduced. The scale has adequate psychometric properties and reflects maximizers' aspirations for high standards and their preference for extensive alternative search, but not the decision difficulty aspect included in several previous studies. Based on this scale, maximizing is positively correlated with optimism, need for cogniti...
Nguyen, Daniel Xuyen
This paper presents a model of trade that explains why firms wait to export and why many exporters fail. Firms face uncertain demands that are only realized after the firm enters the destination. The model retools the timing of uncertainty resolution found in productivity heterogeneity models...... the high rate of exit seen in the first years of exporting. Finally, when faced with multiple countries in which to export, some firms will choose to sequentially export in order to slowly learn more about its chances for success in untested markets....
Quantum information theory mathematical foundation
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...
Thomas, R.E.
1982-03-01
An evaluation is made of the suitability of analytical and statistical sampling methods for making uncertainty analyses. The adjoint method is found to be well-suited for obtaining sensitivity coefficients for computer programs involving large numbers of equations and input parameters. For this purpose the Latin Hypercube Sampling method is found to be inferior to conventional experimental designs. The Latin hypercube method can be used to estimate output probability density functions, but requires supplementary rank transformations followed by stepwise regression to obtain uncertainty information on individual input parameters. A simple Cork and Bottle problem is used to illustrate the efficiency of the adjoint method relative to certain statistical sampling methods. For linear models of the form Ax=b it is shown that a complete adjoint sensitivity analysis can be made without formulating and solving the adjoint problem. This can be done either by using a special type of statistical sampling or by reformulating the primal problem and using suitable linear programming software.
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.
Characterizing maximally singular phase-space distributions
Sperling, J.
2016-07-01
Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.
HEMI: Hyperedge Majority Influence Maximization
Gangal, Varun; Narayanam, Ramasuri
2016-01-01
In this work, we consider the problem of influence maximization on a hypergraph. We first extend the Independent Cascade (IC) model to hypergraphs, and prove that the traditional influence maximization problem remains submodular. We then present a variant of the influence maximization problem (HEMI) where one seeks to maximize the number of hyperedges, a majority of whose nodes are influenced. We prove that HEMI is non-submodular under the diffusion model proposed.
Andersen, Klaus Ejner
1985-01-01
Guinea pig maximization tests (GPMT) with chlorocresol were performed to ascertain whether the sensitization rate was affected by minor changes in the Freund's complete adjuvant (FCA) emulsion used. Three types of emulsion were evaluated: the oil phase was mixed with propylene glycol, saline...... with 30% (v/v) ethanol or saline, respectively. Relative viscosity was used as one measure of physical properties of the emulsion. Higher degrees of sensitization (but not rates) were obtained at the 48 h challenge reading with the oil/propylene glycol and oil/saline + ethanol emulsions compared...... to the saline/oil emulsion. Placing of the challenge patches affected the response, as simultaneous chlorocresol challenge on the flank located 2 cm closer to the abdomen than the usual challenge site gave decreased reactions....
Aspects of complementarity and uncertainty
Vathsan, Radhika; Qureshi, Tabish
2016-08-01
The two-slit experiment with quantum particles provides many insights into the behavior of quantum mechanics, including Bohr’s complementarity principle. Here, we analyze Einstein’s recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert-Greenberger-Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement is an integral part of the which-way detection process, and so is uncertainty, though in a completely different way from that envisaged by Bohr and Einstein.
Uncertainty relations for general unitary operators
Bagchi, Shrobona; Pati, Arun Kumar
2016-10-01
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the uncertainty relation for the unitary operators, we obtain the tight state-independent lower bound for the uncertainty of two Pauli observables and anticommuting observables in higher dimensions. With regard to the minimum-uncertainty states, we derive the minimum-uncertainty state equation by the analytic method and relate this to the ground-state problem of the Harper Hamiltonian. Furthermore, the higher-dimensional limit of the uncertainty relations and minimum-uncertainty states are explored. From an operational point of view, we show that the uncertainty in the unitary operator is directly related to the visibility of quantum interference in an interferometer where one arm of the interferometer is affected by a unitary operator. This shows a principle of preparation uncertainty, i.e., for any quantum system, the amount of visibility for two general noncommuting unitary operators is nontrivially upper bounded.
Generalized uncertainty relations
Herdegen, Andrzej; Ziobro, Piotr
2017-04-01
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly bounded) functions of basic observables usually leads to more complex and less readily interpretable relations. In addition, UR may turn trivial for certain states if the commutator of observables is not proportional to a positive operator. In this letter we consider a generalization of standard UR resulting from the use of two, instead of one, vector states. The possibility to link these states to each other in various ways adds additional flexibility to UR, which may compensate some of the above-mentioned drawbacks. We discuss applications of the general scheme, leading not only to technical improvements, but also to interesting new insight.
MAXIMS VIOLATIONS IN LITERARY WORK
Widya Hanum Sari Pertiwi
2015-12-01
Full Text Available This study was qualitative research action that focuses to find out the flouting of Gricean maxims and the functions of the flouting in the tales which are included in collection of children literature entitled My Giant Treasury of Stories and Rhymes. The objective of the study is generally to identify the violation of maxims of quantity, quality, relevance, and manner in the data sources and also to analyze the use of the flouting in the tales which are included in the book. Qualitative design using categorizing strategies, specifically coding strategy, was applied. Thus, the researcher as the instrument in this investigation was selecting the tales, reading them, and gathering every item which reflects the violation of Gricean maxims based on some conditions of flouting maxims. On the basis of the data analysis, it was found that the some utterances in the tales, both narration and conversation, flouting the four maxims of conversation, namely maxim of quality, maxim of quantity, maxim of relevance, and maxim of manner. The researcher has also found that the flouting of maxims has one basic function that is to encourage the readers’ imagination toward the tales. This one basic function is developed by six others functions: (1 generating specific situation, (2 developing the plot, (3 enlivening the characters’ utterance, (4 implicating message, (5 indirectly characterizing characters, and (6 creating ambiguous setting. Keywords: children literature, tales, flouting maxims
Swanepoel, Konrad J
2011-01-01
A subset of a normed space X is called equilateral if the distance between any two points is the same. Let m(X) be the smallest possible size of an equilateral subset of X maximal with respect to inclusion. We first observe that Petty's construction of a d-dimensional X of any finite dimension d >= 4 with m(X)=4 can be generalised to show that m(X\\oplus_1\\R)=4 for any X of dimension at least 2 which has a smooth point on its unit sphere. By a construction involving Hadamard matrices we then show that both m(\\ell_p) and m(\\ell_p^d) are finite and bounded above by a function of p, for all 1 1 such that m(X) <= d+1 for all d-dimensional X with Banach-Mazur distance less than c from \\ell_p^d. Using Brouwer's fixed-point theorem we show that m(X) <= d+1 for all d-\\dimensional X with Banach-Mazur distance less than 3/2 from \\ell_\\infty^d. A graph-theoretical argument furthermore shows that m(\\ell_\\infty^d)=d+1. The above results lead us to conjecture that m(X) <= 1+\\dim X.
Unified Maximally Natural Supersymmetry
Huang, Junwu
2016-01-01
Maximally Natural Supersymmetry, an unusual weak-scale supersymmetric extension of the Standard Model based upon the inherently higher-dimensional mechanism of Scherk-Schwarz supersymmetry breaking (SSSB), possesses remarkably good fine tuning given present LHC limits. Here we construct a version with precision $SU(2)_{\\rm L} \\times U(1)_{\\rm Y} $ unification: $\\sin^2 \\theta_W(M_Z) \\simeq 0.231$ is predicted to $\\pm 2\\%$ by unifying $SU(2)_{\\rm L} \\times U(1)_{\\rm Y} $ into a 5D $SU(3)_{\\rm EW}$ theory at a Kaluza-Klein scale of $1/R_5 \\sim 4.4\\,{\\rm TeV}$, where SSSB is simultaneously realised. Full unification with $SU(3)_{\\rm C}$ is accommodated by extending the 5D theory to a $N=4$ supersymmetric $SU(6)$ gauge theory on a 6D rectangular orbifold at $1/R_6 \\sim 40 \\,{\\rm TeV}$. TeV-scale states beyond the SM include exotic charged fermions implied by $SU(3)_{\\rm EW}$ with masses lighter than $\\sim 1.2\\,{\\rm TeV}$, and squarks in the mass range $1.4\\,{\\rm TeV} - 2.3\\,{\\rm TeV}$, providing distinct signature...
Duarte, FJ
2013-01-01
Quantum Optics for Engineers provides a transparent and methodical introduction to quantum optics via the Dirac's bra-ket notation with an emphasis on practical applications and basic aspects of quantum mechanics such as Heisenberg's uncertainty principle and Schrodinger's equation. Self-contained and using mainly first-year calculus and algebra tools, the book:Illustrates the interferometric quantum origin of fundamental optical principles such as diffraction, refraction, and reflectionProvides a transparent introduction, via Dirac's notation, to the probability amplitude of quantum entanglem
On Classical and Quantum Cryptography
Volovich, I V; Volovich, Ya.I.
2001-01-01
Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no cloning theorem. The BB84 quantum cryptographic protocol. Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.
Fully nonlocal quantum correlations
Aolita, Leandro; Acín, Antonio; Chiuri, Andrea; Vallone, Giuseppe; Mataloni, Paolo; Cabello, Adán
2011-01-01
Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Previous examples of maximal quantum nonlocality between two parties require an infinite number of measurements, and the corresponding Bell violation is not robust against noise. We show how every proof of the Kochen-Specker theorem gives rise to maximally nonlocal quantum correlations that involve a finite number of measurements and are robust against noise. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content $p_L\\lesssim 0.22$.
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...
Goyal, Ketan; Kawai, Ryoichi
As nanotechnology advances, understanding of the thermodynamic properties of small systems becomes increasingly important. Such systems are found throughout physics, biology, and chemistry manifesting striking properties that are a direct result of their small dimensions where fluctuations become predominant. The standard theory of thermodynamics for macroscopic systems is powerless for such ever fluctuating systems. Furthermore, as small systems are inherently quantum mechanical, influence of quantum effects such as discreteness and quantum entanglement on their thermodynamic properties is of great interest. In particular, the quantum fluctuations due to quantum uncertainty principles may play a significant role. In this talk, we investigate thermodynamic properties of an autonomous quantum heat engine, resembling a quantum version of the Feynman Ratchet, in non-equilibrium condition based on the theory of open quantum systems. The heat engine consists of multiple subsystems individually contacted to different thermal environments.
Hypothesis testing with open quantum systems.
Mølmer, Klaus
2015-01-30
Using a quantum circuit model we derive the maximal ability to distinguish which of several candidate Hamiltonians describe an open quantum system. This theory, in particular, provides the maximum information retrievable from continuous quantum measurement records, available when a quantum system is perturbatively coupled to a broadband quantized environment.
Maximal-acceleration phase space relativity from Clifford algebras
Castro, C
2002-01-01
We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). Crucial in order to establish this link is the use of Clifford algebras in phase spaces. The maximal proper-acceleration bound is a = c^2/ \\Lambda in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. We present the reasons why an Extended Scale Relativity based on Clifford spaces is physically more appealing than those based on kappa-deformed Poincare algebras and the inhomogeneous quantum groups operating in quantum Minkowski spacetimes. The main reason being that the Planck scale should not be taken as a deformation parameter to construct quantum algebras but should exist already as the minimum scale in Clifford spaces.
Maximal subgroups of finite groups
S. Srinivasan
1990-01-01
Full Text Available In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting subgroup of the group.
Optimization of quantum interferometric metrological sensors in the presence of photon loss
Lee, Tae-Woo; Lee, Hwang; Kaplan, Lev; McCracken, Steven B; Min, Changjun; Uskov, Dmitry B; Wildfeuer, Christoph F; Veronis, Georgios; Dowling, Jonathan P
2009-01-01
We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.
MicroBlack Holes Thermodynamics in the Presence of Quantum Gravity Effects
H. Soltani
2014-01-01
Full Text Available Black hole thermodynamics is corrected in the presence of quantum gravity effects. Some phenomenological aspects of quantum gravity proposal can be addressed through generalized uncertainty principle (GUP which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of both a minimal measurable length and a maximal momentum on the thermodynamics of TeV-scale black holes. We then extend our study to the case that there are all natural cutoffs as minimal length, minimal momentum, and maximal momentum simultaneously. We also generalize our study to the model universes with large extra dimensions (LED. In this framework existence of black holes remnants as a possible candidate for dark matter is discussed. We study probability of black hole production in the Large Hadronic Collider (LHC and we show this rate decreasing for sufficiently large values of the GUP parameter.
Finding Maximal Quasiperiodicities in Strings
Brodal, Gerth Stølting; Pedersen, Christian N. S.
2000-01-01
of length n in time O(n log n) and space O(n). Our algorithm uses the suffix tree as the fundamental data structure combined with efficient methods for merging and performing multiple searches in search trees. Besides finding all maximal quasiperiodic substrings, our algorithm also marks the nodes......Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic substring and gave an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log2 n). In this paper we give an algorithm that finds all maximal quasiperiodic substrings in a string...
Maximizing Entropy over Markov Processes
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Maximizing entropy over Markov processes
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Popper's Experiment and the Uncertainty Principle
Cardoso, António
2015-01-01
In this paper we look at a particular realization of Popper's thought experiment with correlated quantum particles and argue that, from the point of view of a nonlinear quantum physics and contrary to the orthodox interpretation, Heisenberg's uncertainty principle is violated. Moreover, we show that this kind of experiments can easily be explained in an intuitive manner if we are willing to take a nonlinear approach.
Non-scalar uncertainty: Uncertainty in dynamic systems
Martinez, Salvador Gutierrez
1992-01-01
The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an
Minimum Uncertainty, Coherence and Squeezing in Diffusion Processes, and Stochastic Quantization
De Martino, S; Illuminati, F; Vitiello, G; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio; Vitiello, Giuseppe
1993-01-01
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
The effect of quantum noise on multiplayer quantum game
Cao Shuai; Fang Mao-Fa; Zheng Xiao-Juan
2007-01-01
It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games.However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0 (≤) p (≤) 0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622 ＜ p (≤) 1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.
Quantum Aspects of the GP Model.
Wood, William Robert
In this thesis, the possibility that the description of Nature provided by the theories of general relativity and quantum mechanics may be made more complete by incorporating the ideas of the causal interpretation of quantum mechanics into a conformally invariant theory in Weyl space is investigated. The unified theory of gravitation and electromagnetism provided by the Gregorash-Papini (GP) model is shown to support both the particle and wave aspects required in the causal interpretation, as well as a nonlinear Klein-Gordon wave equation. The Gauss-Mainardi-Codazzi formalism is developed in Weyl geometry and then used to construct a particle model in terms of a spherically symmetric thin shell with a scalar-field-induced surface stress-energy tensor. By breaking the interior Weyl invariance at the microscopic scale, a new means by which Weyl's geometric interpretation of the exterior electromagnetic field may be reconciled with atomic standards of length becomes possible. In addition, the properties of the resulting interior anti-de Sitter space may prove to play an important role in accounting for the nonlocal effects that are necessarily present in any causal interpretation. The particle, which is represented by the thin shell, is embedded in the exterior Madelung fluid of the GP model such that de Broglie's guidance principle is satisfied. It is argued that a proper analysis of the guidance mechanism hypothesized in the causal interpretation is possible only in a geometrical formulation. The possibility that the causal theory that is developed in Weyl space requires a maximal acceleration is also investigated. A limiting acceleration has recently been shown to arise in other theories when aspects of quantum mechanics, such as the uncertainty relations, are employed. A controversial derivation based on the time-energy uncertainty relation is clarified and two new arguments for a maximal acceleration are presented. Finally, the demonstration that the causal
Gonzalez-Sanchez, Jon
2010-01-01
Let $w = w(x_1,..., x_n)$ be a word, i.e. an element of the free group $F =$ on $n$ generators $x_1,..., x_n$. The verbal subgroup $w(G)$ of a group $G$ is the subgroup generated by the set $\\{w (g_1,...,g_n)^{\\pm 1} | g_i \\in G, 1\\leq i\\leq n \\}$ of all $w$-values in $G$. We say that a (finite) group $G$ is $w$-maximal if $|G:w(G)|> |H:w(H)|$ for all proper subgroups $H$ of $G$ and that $G$ is hereditarily $w$-maximal if every subgroup of $G$ is $w$-maximal. In this text we study $w$-maximal and hereditarily $w$-maximal (finite) groups.
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Information Geometry of Quantum Entangled Gaussian Wave-Packets
Kim, D -H; Cafaro, C; Mancini, S
2011-01-01
Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. We use the statistical manifolds associated with correlated and non-correlated Gaussians to model the scattering induced quantum entanglement of two spinless, structureless, non-relativistic particles, the latter represented by minimum uncertainty Gaussian wave-packets. Knowing that the degree of entanglement is quantified by the purity P of the system, we express the purity for s-wave scattering in terms of the micro-correlation coefficient r - a quantity that parameterizes the correlated microscopic degrees of freedom of the system; thus establishing a connection between entanglement and micro-correlations. Moreover, ...
Identification and communication of uncertainties of phenomenological models in PSA
Pulkkinen, U.; Simola, K. [VTT Automation (Finland)
2001-11-01
This report aims at presenting a view upon uncertainty analysis of phenomenological models with an emphasis on the identification and documentation of various types of uncertainties and assumptions in the modelling of the phenomena. In an uncertainty analysis, it is essential to include and document all unclear issues, in order to obtain a maximal coverage of unresolved issues. This holds independently on their nature or type of the issues. The classification of uncertainties is needed in the decomposition of the problem and it helps in the identification of means for uncertainty reduction. Further, an enhanced documentation serves to evaluate the applicability of the results to various risk-informed applications. (au)
Maximizing without difficulty: A modified maximizing scale and its correlates
Lai, Linda
2010-01-01
... included in several previous studies. Based on this scale, maximizing is positively correlated with optimism, need for cognition, desire for consistency, risk aversion, intrinsic motivation, self-efficacy and perceived workload, whereas...
Maximizing and customer loyalty: Are maximizers less loyal?
Linda Lai
2011-06-01
Full Text Available Despite their efforts to choose the best of all available solutions, maximizers seem to be more inclined than satisficers to regret their choices and to experience post-decisional dissonance. Maximizers may therefore be expected to change their decisions more frequently and hence exhibit lower customer loyalty to providers of products and services compared to satisficers. Findings from the study reported here (N = 1978 support this prediction. Maximizers reported significantly higher intentions to switch to another service provider (television provider than satisficers. Maximizers' intentions to switch appear to be intensified and mediated by higher proneness to regret, increased desire to discuss relevant choices with others, higher levels of perceived knowledge of alternatives, and higher ego involvement in the end product, compared to satisficers. Opportunities for future research are suggested.
Are maximizers really unhappy? The measurement of maximizing tendency,
Dalia L. Diab
2008-06-01
Full Text Available Recent research suggesting that people who maximize are less happy than those who satisfice has received considerable fanfare. The current study investigates whether this conclusion reflects the construct itself or rather how it is measured. We developed an alternative measure of maximizing tendency that is theory-based, has good psychometric properties, and predicts behavioral outcomes. In contrast to the existing maximization measure, our new measure did not correlate with life (dissatisfaction, nor with most maladaptive personality and decision-making traits. We conclude that the interpretation of maximizers as unhappy may be due to poor measurement of the construct. We present a more reliable and valid measure for future researchers to use.
Do the Uncertainty Relations Really have Crucial Significances for Physics?
Dumitru S.
2010-10-01
Full Text Available It is proved the falsity of idea that the Uncertainty Relations (UR have crucial significances for physics. Additionally one argues for the necesity of an UR-disconnected quantum philosophy.
Time Crystals from Minimum Time Uncertainty
Faizal, Mir; Das, Saurya
2016-01-01
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra, and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal.
Generalized Uncertainty Principle: Implications for Black Hole Complementarity
Chen, Pisin; Yeom, Dong-han
2014-01-01
At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg's Uncertainty Principle, the application of GUP may save complementarity, but only if certain N-dependence is also assumed. This rais...
Statistical features of quantum evolution
Sudhir R Jain
2009-08-01
It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian of the quantum system for an arbitrary pseudo-unitary (and hence $\\mathcal{PT}$ -) quantum evolution. The result generalizes the time– energy uncertainty principle for pseudo-unitary quantum evolutions. Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that can be modelled by random matrix theory.
Robust Adaptive Quantum Phase Estimation
Roy, Shibdas; Huntington, Elanor H
2014-01-01
Quantum parameter estimation is central to many fields such as quantum computation, communications and metrology. Optimal estimation theory has been instrumental in achieving the best accuracy in quantum parameter estimation, which is possible when we have very precise knowledge of and control over the model. However, uncertainties in key parameters underlying the system are unavoidable and may impact the quality of the estimate. We show here how quantum optical phase estimation of a squeezed state of light exhibits improvement when using a robust fixed-interval smoother designed with uncertainties explicitly introduced in parameters underlying the phase noise.
Quantum metrology in coarsened measurement reference
Xie, Dong; Xu, Chunling; Wang, An Min
2017-01-01
We investigate the role of coarsened measurement reference, which originates from the coarsened reference time and basis, in quantum metrology. When the measurement is based on one common reference basis, the disadvantage of coarsened measurement can be removed by symmetry. Owing to the coarsened reference basis, the entangled state cannot perform better than the product state for a large number of probe particles in estimating the phase. Given a finite uncertainty of the coarsened reference basis, the optimal number of probe particles is obtained. Finally, we prove that the maximally entangled state always achieves better frequency precision in the case of non-Markovian dephasing than that in the case of Markovian dephasing. The product state is more resistant to the interference of the coarsened reference time than the entangled state.
Maximizing ROI with yield management
Neil Snyder
2001-01-01
.... the technology is based on the concept of yield management, which aims to sell the right product to the right customer at the right price and the right time therefore maximizing revenue, or yield...
All maximally entangling unitary operators
Cohen, Scott M. [Department of Physics, Duquesne University, Pittsburgh, Pennsylvania 15282 (United States); Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 (United States)
2011-11-15
We characterize all maximally entangling bipartite unitary operators, acting on systems A and B of arbitrary finite dimensions d{sub A}{<=}d{sub B}, when ancillary systems are available to both parties. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when d{sub A}=d{sub B}.
Salvio, Alberto; Strumia, Alessandro; Urbano, Alfredo
2016-01-01
Motivated by the 750 GeV diphoton excess found at LHC, we compute the maximal width into $\\gamma\\gamma$ that a neutral scalar can acquire through a loop of charged fermions or scalars as function of the maximal scale at which the theory holds, taking into account vacuum (meta)stability bounds. We show how an extra gauge symmetry can qualitatively weaken such bounds, and explore collider probes and connections with Dark Matter.
Heisenberg Uncertainty Relation in Quantum Liouville Equation
Davide Valenti
2009-01-01
Fourier transform of the density matrix ρ(z,y,t = ψ∗(z,tψ(y,t. We find again that the variances of x and v obtained by using ρ(z, y,t are respectively equal to the variances of X^ and P^ calculated in ψ(x,t. Finally we introduce the matrix ∥Ann′(t∥ and we show that a generic square-integrable function g(x,v,t can be written as Fourier transform of a density matrix, provided that the matrix ∥Ann′(t∥ is diagonalizable.
Verification of uncertainty budgets
Heydorn, Kaj; Madsen, B.S.
2005-01-01
The quality of analytical results is expressed by their uncertainty, as it is estimated on the basis of an uncertainty budget; little effort is, however, often spent on ascertaining the quality of the uncertainty budget. The uncertainty budget is based on circumstantial or historical data, and th...
Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik, Theoretische Elementarteilchenphysik
2013-11-01
New edition with added sections on nonlinear quantum mechanics and path integral methods in field theory. Contains an encyclopedic coverage from uncertainty relation to many-body systems, from symmetries to electroweak interation. Includes problems, partly with solutions, partly with hints towards solutions. Starting with basic principles and providing the framework all vital elements of nonrelativistic quantum mechanics are explained, even an introduction to quantum electrodynamics is included. Scheck's Quantum Physics presents a comprehensive introductory treatment, ideally suited for a two-semester course. Part One covers the basic principles and prime applications of quantum mechanics, from the uncertainty relations to many-body systems. Part Two introduces to relativistic quantum field theory and ranges from symmetries in quantum physics to electroweak interactions. Numerous worked-out examples as well as exercises, with solutions or hints, enables the book's use as an accompanying text for courses, and also for independent study. For both parts, the necessary mathematical framework is treated in adequate form and detail. The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory. The new edition was thoroughly revised and now includes new sections on quantization using the path integral method and on deriving generalized path integrals for bosonic and fermionic fields.
FAN Hong-Yi; SUN Zhi-Hu
2000-01-01
For the Noh, Fougères and Mandel (NFM) operational quantum phase description, which is based on an eightport homodyne-detection, we derive the minimum uncertainty states for the number-difference-phase uncertainty relation. The derivation makes full use of the newly constructed ｜q, τ) representation which is the common eigenvector of the two-mode photon number-difference a+a -b+b and (a + b+)(a+ + b)
Quantum aspects of the GP model. [GP (Gregorash-Papini)
Wood, W.R.
1992-01-01
The possibility that the description of Nature provided by the theories of general relativity and quantum mechanics may be made more complete by incorporating the ideas of the causal interpretation of quantum mechanics into a conformally invariant theory in Weyl space is investigated. The unified theory of gravitation and electromagnetism provided by the Gregorash-Papini (GP) model is shown to support both the particle and wave aspects required in the causal interpretation, as well as a nonlinear Klein-Gordon wave equation. The Gauss-Mainardi-Codazzi formalism is developed in Weyl geometry and used to construct a particle model in terms of a spherically symmetry thin shell with a scalar-field-induced surface stress-energy tensor. By breaking the interior Weyl invariance at the microscopic scale, a new means by which Weyl's geometric interpretation of the exterior electromagnetic field may be reconciled with atomic standards of length becomes possible. The properties of the resulting interior anti-de Sitter space may play an important role in accounting for the nonlocal effects that are present in any causal interpretation. The particle, represented by the thin shell, is embedded in the exterior Madelung fluid of the GP model such that de Broglie's guidance principle is satisfied. It is argued that a proper analysis of the guidance mechanism hypothesized in the causal interpretation is possible only in a geometrical formulation. The possibility that the causal theory developed in Weyl space requires a maximal acceleration is investigated. A limiting acceleration arises in other theories when aspects of quantum mechanics are employed. A controversial derivation based on the time-energy uncertainty relation is clarified and two new arguments for a maximal acceleration are presented. The demonstration that the causal theory in Weyl space also requires a maximal acceleration supports the view that it is possible to provide a spacetime description of quantum
Quantum coherence of steered states
Hu, Xueyuan; Milne, Antony; Zhang, Boyang; Fan, Heng
2016-01-01
Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schödinger, has also recently received much attention. When Alice and Bob share a correlated quantum system, Alice can perform a local measurement to ‘steer’ Bob’s reduced state. We introduce the maximal steered coherence as a measure describing the extent to which steering can remotely create coherence; more precisely, we find the maximal coherence of Bob’s steered state in the eigenbasis of his original reduced state, where maximization is performed over all positive-operator valued measurements for Alice. We prove that maximal steered coherence vanishes for quantum-classical states whilst reaching a maximum for pure entangled states with full Schmidt rank. Although invariant under local unitary operations, maximal steered coherence may be increased when Bob performs a channel. For a two-qubit state we find that Bob’s channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical, which coincides with the condition for increasing discord. Our results show that the power of steering for coherence generation, though related to discord, is distinct from existing measures of quantum correlation.
New entropic uncertainty relations for prime power dimensions
Funder, Jakob Løvstad
2011-01-01
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple probability distributions under the constraint that the sum...
Sassoli de Bianchi, Massimiliano, E-mail: autoricerca@gmail.com
2013-09-15
In a letter to Born, Einstein wrote [42]: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.” In this paper we take seriously Einstein’s famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell’s inequality. -- Highlights: •Rolling a die is a quantum process admitting a Hilbert space representation. •Rolling experiments with a single die can produce interference effects. •Two connected dice can violate Bell’s inequality. •Correlations need to be created by the measurement, to violate Bell’s inequality.
Nonlocality of quantum correlations
Streltsov, A; Roga, W; Bruß, D; Illuminati, F
2012-01-01
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. This type of nonlocality occurs also for states that do not violate a Bell inequality, such as, for instance, Werner states with a low degree of entanglement. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord, thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish rigorously that Werner states are the maximally quantum correlated two-qubit states, and thus are the ones that maximize this novel type of nonlocality.
Fine-grained uncertainty relation under the relativistic motion
Feng, Jun; Gould, Mark D; Fan, Heng
2014-01-01
One of the most important features of quantum theory is the uncertainty principle. Amount various uncertainty relations, the profound Fine-Grained Uncertainty Relation (FGUR) is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this paper, we explore this uncertainty relation in relativistic regime. For observer undergoes an uniform acceleration who immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and choice of Unruh modes. Dramatically, we find that the measurements in Mutually Unbiased Bases (MUBs), sharing same uncertainty bound in inertial frame, could be distinguished from each other for a noninertial observer. On the other hand, once the Unruh decoherence is prevented by utilizing the cavity, the entanglement could be generated from nonuniform motion. We show that, for the observer restricted in a single rigid cavity, the uncertainty exhibits a periodic evolution with respec...
Rossi, Matteo A C; Paris, Matteo G A
2016-01-01
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be described by introducing a modified position-momentum commutator, which in turn yields a generalized uncertainty principle, where the uncertainty on the position measurement has a lower bound. The value of the minimal length is not predicted by theories and must be evaluated experimentally. In this paper, we address the quantum bound to estimability of the minimal uncertainty length by performing measurements on a harmonic oscillator, which is analytically solvable in the deformed algebra of the Hilbert subspace.
Some Implications of Two Forms of the Generalized Uncertainty Principle
Mohammed M. Khalil
2014-01-01
Full Text Available Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP. In this paper, we study two forms of the GUP and calculate their implications on the energy of the harmonic oscillator and the hydrogen atom more accurately than previous studies. In addition, we show how the GUP modifies the Lorentz force law and the time-energy uncertainty principle.
Uncertainty Estimates for Theoretical Atomic and Molecular Data
Chung, H -K; Bartschat, K; Csaszar, A G; Drake, G W F; Kirchner, T; Kokoouline, V; Tennyson, J
2016-01-01
Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We concentrate on model uncertainties due to approximations to the fundamental many-body quantum mechanical equations and we aim to provide guidelines to estimate uncertainties as a routine part of computations of data for structure and scattering.
A. Garmroodi Asil
2017-09-01
To further reduce the sulfur dioxide emission of the entire refining process, two scenarios of acid gas or air preheats are investigated when either of them is used simultaneously with the third enrichment scheme. The maximum overall sulfur recovery efficiency and highest combustion chamber temperature is slightly higher for acid gas preheats but air preheat is more favorable because it is more benign. To the best of our knowledge, optimization of the entire GTU + enrichment section and SRU processes has not been addressed previously.
Algebraic curves of maximal cyclicity
Caubergh, Magdalena; Dumortier, Freddy
2006-01-01
The paper deals with analytic families of planar vector fields, studying methods to detect the cyclicity of a non-isolated closed orbit, i.e. the maximum number of limit cycles that can locally bifurcate from it. It is known that this multi-parameter problem can be reduced to a single-parameter one, in the sense that there exist analytic curves in parameter space along which the maximal cyclicity can be attained. In that case one speaks about a maximal cyclicity curve (mcc) in case only the number is considered and of a maximal multiplicity curve (mmc) in case the multiplicity is also taken into account. In view of obtaining efficient algorithms for detecting the cyclicity, we investigate whether such mcc or mmc can be algebraic or even linear depending on certain general properties of the families or of their associated Bautin ideal. In any case by well chosen examples we show that prudence is appropriate.
USTC Experiment Verifies Entanglement-assisted Entropic Uncertainty Principle
SONG Jianlan
2011-01-01
@@ The entanglement-assisted entropic uncertainty principle, a new violation of the classical version of uncertainty principle established by Werner Heisenberg, was recently confirmed through an experimental investigation by a group of physicists at the Key Laboratory of Quantum Information under the University of Science and Technology of China (USTC).This experiment, published in the journal Nature Physics, revealed that the classical"Heisenberg-Robertson uncertainty relation" could be violated, on condition that the quantum information of the particle of interest is previously stored by its twin particle, to which it is fully entangled.
The Black Hole Uncertainty Principle Correspondence
Carr, B J
2014-01-01
The Black Hole Uncertainty Principle correspondence proposes a connection between the Uncertainty Principle on microscopic scales and black holes on macroscopic scales. This is manifested in a unified expression for the Compton wavelength and Schwarzschild radius. It is a natural consequence of the Generalized Uncertainty Principle, which suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It also entails corrections to the event horizon size as the black hole mass falls to the Planck value, leading to the concept of a Generalized Event Horizon. One implication of this is that there could be sub-Planckian black holes with a size of order their Compton wavelength. Loop quantum gravity suggests the existence of black holes with precisely this feature. The correspondence leads to a heuristic derivation of the black hole temperature and suggests how the Hawking formula is modified in the sub-Planckian regime.
BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS
CHEN JIECHENG; ZHU XIANGRONG
2005-01-01
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itseff, it is proved that the maximal singu lar integral is bounded from L∞ to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.
Optimal compensation for temporal uncertainty in movement planning.
Todd E Hudson
2008-07-01
Full Text Available Motor control requires the generation of a precise temporal sequence of control signals sent to the skeletal musculature. We describe an experiment that, for good performance, requires human subjects to plan movements taking into account uncertainty in their movement duration and the increase in that uncertainty with increasing movement duration. We do this by rewarding movements performed within a specified time window, and penalizing slower movements in some conditions and faster movements in others. Our results indicate that subjects compensated for their natural duration-dependent temporal uncertainty as well as an overall increase in temporal uncertainty that was imposed experimentally. Their compensation for temporal uncertainty, both the natural duration-dependent and imposed overall components, was nearly optimal in the sense of maximizing expected gain in the task. The motor system is able to model its temporal uncertainty and compensate for that uncertainty so as to optimize the consequences of movement.
Robust Quantum Error Correction via Convex Optimization
Kosut, R L; Lidar, D A
2007-01-01
Quantum error correction procedures have traditionally been developed for specific error models, and are not robust against uncertainty in the errors. Using a semidefinite program optimization approach we find high fidelity quantum error correction procedures which present robust encoding and recovery effective against significant uncertainty in the error system. We present numerical examples for 3, 5, and 7-qubit codes. Our approach requires as input a description of the error channel, which can be provided via quantum process tomography.
Nanoparticles: Uncertainty Risk Analysis
Grieger, Khara Deanne; Hansen, Steffen Foss; Baun, Anders
2012-01-01
Scientific uncertainty plays a major role in assessing the potential environmental risks of nanoparticles. Moreover, there is uncertainty within fundamental data and information regarding the potential environmental and health risks of nanoparticles, hampering risk assessments based on standard a...
Understanding maximal repetitions in strings
Crochemore, Maxime
2008-01-01
The cornerstone of any algorithm computing all repetitions in a string of length n in O(n) time is the fact that the number of runs (or maximal repetitions) is O(n). We give a simple proof of this result. As a consequence of our approach, the stronger result concerning the linearity of the sum of exponents of all runs follows easily.
Quantum cryptography using optical fibers.
Franson, J D; Lives, H
1994-05-10
Quantum cryptography permits the transmission of secret information whose security is guaranteed by the uncertainty principle. An experimental system for quantum crytography is implemented based on the linear polarization of single photons transmitted by an optical fiber. Polarization-preserving optical fiber and a feedback loop are employed to maintain the state of polarization. Error rates of less than 0.5% are obtained.
Reformulating and Reconstructing Quantum Theory
Hardy, Lucien
2011-01-01
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of positive operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutatability. There exis...
A violation of the uncertainty principle implies a violation of the second law of thermodynamics.
Hänggi, Esther; Wehner, Stephanie
2013-01-01
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? Here we give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.
The equivalence principle in a quantum world
Bjerrum-Bohr, N. Emil J.; Donoghue, John F.; El-Menoufi, Basem Kamal
2015-01-01
We show how modern methods can be applied to quantum gravity at low energy. We test how quantum corrections challenge the classical framework behind the equivalence principle (EP), for instance through introduction of nonlocality from quantum physics, embodied in the uncertainty principle. When t...... (EFT)....
Optical Model and Cross Section Uncertainties
Herman,M.W.; Pigni, M.T.; Dietrich, F.S.; Oblozinsky, P.
2009-10-05
Distinct minima and maxima in the neutron total cross section uncertainties were observed in model calculations using spherical optical potential. We found this oscillating structure to be a general feature of quantum mechanical wave scattering. Specifically, we analyzed neutron interaction with 56Fe from 1 keV up to 65 MeV, and investigated physical origin of the minima.We discuss their potential importance for practical applications as well as the implications for the uncertainties in total and absorption cross sections.
Parton Distribution Function Uncertainties
Giele, Walter T.; Kosower, David A.; Giele, Walter T.; Keller, Stephane A.; Kosower, David A.
2001-01-01
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density measure over the functional space of parton distribution functions. This leads to a convenient method of propagating the parton distribution function uncertainties to new observables, now expressing the uncertainty as a density in the prediction of the observable. New measurements can easily be included in the optimized sets as added weight functions to the density measure. Using the optimized method nowhere in the analysis compromises have to be made with regard to the treatment of the uncertainties.
Predictive uncertainty in auditory sequence processing.
Hansen, Niels Chr; Pearce, Marcus T
2014-01-01
Previous studies of auditory expectation have focused on the expectedness perceived by listeners retrospectively in response to events. In contrast, this research examines predictive uncertainty-a property of listeners' prospective state of expectation prior to the onset of an event. We examine the information-theoretic concept of Shannon entropy as a model of predictive uncertainty in music cognition. This is motivated by the Statistical Learning Hypothesis, which proposes that schematic expectations reflect probabilistic relationships between sensory events learned implicitly through exposure. Using probability estimates from an unsupervised, variable-order Markov model, 12 melodic contexts high in entropy and 12 melodic contexts low in entropy were selected from two musical repertoires differing in structural complexity (simple and complex). Musicians and non-musicians listened to the stimuli and provided explicit judgments of perceived uncertainty (explicit uncertainty). We also examined an indirect measure of uncertainty computed as the entropy of expectedness distributions obtained using a classical probe-tone paradigm where listeners rated the perceived expectedness of the final note in a melodic sequence (inferred uncertainty). Finally, we simulate listeners' perception of expectedness and uncertainty using computational models of auditory expectation. A detailed model comparison indicates which model parameters maximize fit to the data and how they compare to existing models in the literature. The results show that listeners experience greater uncertainty in high-entropy musical contexts than low-entropy contexts. This effect is particularly apparent for inferred uncertainty and is stronger in musicians than non-musicians. Consistent with the Statistical Learning Hypothesis, the results suggest that increased domain-relevant training is associated with an increasingly accurate cognitive model of probabilistic structure in music.
Predictive uncertainty in auditory sequence processing
Niels Chr. eHansen
2014-09-01
Full Text Available Previous studies of auditory expectation have focused on the expectedness perceived by listeners retrospectively in response to events. In contrast, this research examines predictive uncertainty - a property of listeners’ prospective state of expectation prior to the onset of an event. We examine the information-theoretic concept of Shannon entropy as a model of predictive uncertainty in music cognition. This is motivated by the Statistical Learning Hypothesis, which proposes that schematic expectations reflect probabilistic relationships between sensory events learned implicitly through exposure.Using probability estimates from an unsupervised, variable-order Markov model, 12 melodic contexts high in entropy and 12 melodic contexts low in entropy were selected from two musical repertoires differing in structural complexity (simple and complex. Musicians and non-musicians listened to the stimuli and provided explicit judgments of perceived uncertainty (explicit uncertainty. We also examined an indirect measure of uncertainty computed as the entropy of expectedness distributions obtained using a classical probe-tone paradigm where listeners rated the perceived expectedness of the final note in a melodic sequence (inferred uncertainty. Finally, we simulate listeners’ perception of expectedness and uncertainty using computational models of auditory expectation. A detailed model comparison indicates which model parameters maximize fit to the data and how they compare to existing models in the literature.The results show that listeners experience greater uncertainty in high-entropy musical contexts than low-entropy contexts. This effect is particularly apparent for inferred uncertainty and is stronger in musicians than non-musicians. Consistent with the Statistical Learning Hypothesis, the results suggest that increased domain-relevant training is associated with an increasingly accurate cognitive model of probabilistic structure in music.
Andres, T.H
2002-05-01
This guide applies to the estimation of uncertainty in quantities calculated by scientific, analysis and design computer programs that fall within the scope of AECL's software quality assurance (SQA) manual. The guide weaves together rational approaches from the SQA manual and three other diverse sources: (a) the CSAU (Code Scaling, Applicability, and Uncertainty) evaluation methodology; (b) the ISO Guide,for the Expression of Uncertainty in Measurement; and (c) the SVA (Systems Variability Analysis) method of risk analysis. This report describes the manner by which random and systematic uncertainties in calculated quantities can be estimated and expressed. Random uncertainty in model output can be attributed to uncertainties of inputs. The propagation of these uncertainties through a computer model can be represented in a variety of ways, including exact calculations, series approximations and Monte Carlo methods. Systematic uncertainties emerge from the development of the computer model itself, through simplifications and conservatisms, for example. These must be estimated and combined with random uncertainties to determine the combined uncertainty in a model output. This report also addresses the method by which uncertainties should be employed in code validation, in order to determine whether experiments and simulations agree, and whether or not a code satisfies the required tolerance for its application. (author)
Uncertainty and Cognitive Control
Faisal eMushtaq
2011-10-01
Full Text Available A growing trend of neuroimaging, behavioural and computational research has investigated the topic of outcome uncertainty in decision-making. Although evidence to date indicates that humans are very effective in learning to adapt to uncertain situations, the nature of the specific cognitive processes involved in the adaptation to uncertainty are still a matter of debate. In this article, we reviewed evidence suggesting that cognitive control processes are at the heart of uncertainty in decision-making contexts. Available evidence suggests that: (1 There is a strong conceptual overlap between the constructs of uncertainty and cognitive control; (2 There is a remarkable overlap between the neural networks associated with uncertainty and the brain networks subserving cognitive control; (3 The perception and estimation of uncertainty might play a key role in monitoring processes and the evaluation of the need for control; (4 Potential interactions between uncertainty and cognitive control might play a significant role in several affective disorders.
Note on maximal distance separable codes
YANG Jian-sheng; WANG De-xiu; JIN Qing-fang
2009-01-01
In this paper, the maximal length of maximal distance separable(MDS)codes is studied, and a new upper bound formula of the maximal length of MDS codes is obtained. Especially, the exact values of the maximal length of MDS codes in some parameters are given.
Maximization, learning, and economic behavior.
Erev, Ido; Roth, Alvin E
2014-07-22
The rationality assumption that underlies mainstream economic theory has proved to be a useful approximation, despite the fact that systematic violations to its predictions can be found. That is, the assumption of rational behavior is useful in understanding the ways in which many successful economic institutions function, although it is also true that actual human behavior falls systematically short of perfect rationality. We consider a possible explanation of this apparent inconsistency, suggesting that mechanisms that rest on the rationality assumption are likely to be successful when they create an environment in which the behavior they try to facilitate leads to the best payoff for all agents on average, and most of the time. Review of basic learning research suggests that, under these conditions, people quickly learn to maximize expected return. This review also shows that there are many situations in which experience does not increase maximization. In many cases, experience leads people to underweight rare events. In addition, the current paper suggests that it is convenient to distinguish between two behavioral approaches to improve economic analyses. The first, and more conventional approach among behavioral economists and psychologists interested in judgment and decision making, highlights violations of the rational model and proposes descriptive models that capture these violations. The second approach studies human learning to clarify the conditions under which people quickly learn to maximize expected return. The current review highlights one set of conditions of this type and shows how the understanding of these conditions can facilitate market design.
Learning robust pulses for generating universal quantum gates
Dong, Daoyi; Wu, Chengzhi; Chen, Chunlin; Qi, Bo; Petersen, Ian R.; Nori, Franco
2016-01-01
Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates. PMID:27782219
Phenomenological Implications of the Generalized Uncertainty Principle
Das, Saurya
2009-01-01
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to \\beta p^4 and \\beta^2 p^6 respectively, where \\beta \\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a Scanning Tunnel Microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.
Reveal quantum correlation in complementary bases
Shengjun Wu; Zhihao Ma; Zhihua Chen; Sixia Yu
2013-01-01
An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a bipartite quantum state, the classical correlation is the maximal correlation present in a certain optimum basis, while the quantum correlation is characterized as a series of residual correlations in the mutually unbiased bases. Compared with other approaches ...
Sixth International Conference on Squeezed States and Uncertainty Relations
Han, D. (Editor); Kim, Y. S. (Editor); Solimento, S. (Editor)
2000-01-01
These proceedings contain contributions from about 200 participants to the 6th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'99) held in Naples May 24-29, 1999, and organized jointly by the University of Naples "Federico II," the University of Maryland at College Park, and the Lebedev Institute, Moscow. This was the sixth of a series of very successful meetings started in 1990 at the College Park Campus of the University of Maryland. The other meetings in the series were held in Moscow (1992), Baltimore (1993), Taiyuan P.R.C. (1995) and Balatonfuered, Hungary (1997). The present one was held at the campus Monte Sant'Angelo of the University "Federico II" of Naples. The meeting sought to provide a forum for updating and reviewing a wide range of quantum optics disciplines, including device developments and applications, and related areas of quantum measurements and quantum noise. Over the years, the ICSSUR Conference evolved from a meeting on quantum measurement sector of quantum optics, to a wide range of quantum optics themes, including multifacet aspects of generation, measurement, and applications of nonclassical light (squeezed and Schrodinger cat radiation fields, etc.), and encompassing several related areas, ranging from quantum measurement to quantum noise. ICSSUR'99 brought together about 250 people active in the field of quantum optics, with special emphasis on nonclassical light sources and related areas. The Conference was organized in 8 Sections: Squeezed states and uncertainty relations; Harmonic oscillators and squeeze transformations; Methods of quantum interference and correlations; Quantum measurements; Generation and characterisation of non-classical light; Quantum noise; Quantum communication and information; and Quantum-like systems.
Time crystals from minimum time uncertainty
Faizal, Mir; Khalil, Mohammed M.; Das, Saurya
2016-01-01
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal. As an application of our formalism, we analyze the effect of such a deformation on the rate of spontaneous emission in a hydrogen atom.
Time crystals from minimum time uncertainty
Faizal, Mir [University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada); Khalil, Mohammed M. [Alexandria University, Department of Electrical Engineering, Alexandria (Egypt); Das, Saurya [University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada)
2016-01-15
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal. As an application of our formalism, we analyze the effect of such a deformation on the rate of spontaneous emission in a hydrogen atom. (orig.)
Uncertain LDA: Including Observation Uncertainties in Discriminative Transforms.
Saeidi, Rahim; Astudillo, Ramon Fernandez; Kolossa, Dorothea
2016-07-01
Linear discriminant analysis (LDA) is a powerful technique in pattern recognition to reduce the dimensionality of data vectors. It maximizes discriminability by retaining only those directions that minimize the ratio of within-class and between-class variance. In this paper, using the same principles as for conventional LDA, we propose to employ uncertainties of the noisy or distorted input data in order to estimate maximally discriminant directions. We demonstrate the efficiency of the proposed uncertain LDA on two applications using state-of-the-art techniques. First, we experiment with an automatic speech recognition task, in which the uncertainty of observations is imposed by real-world additive noise. Next, we examine a full-scale speaker recognition system, considering the utterance duration as the source of uncertainty in authenticating a speaker. The experimental results show that when employing an appropriate uncertainty estimation algorithm, uncertain LDA outperforms its conventional LDA counterpart.
Generalized Geometric Quantum Speed Limits
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Generalized Geometric Quantum Speed Limits
Diego Paiva Pires
2016-06-01
Full Text Available The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Uncertainty in artificial intelligence
Kanal, LN
1986-01-01
How to deal with uncertainty is a subject of much controversy in Artificial Intelligence. This volume brings together a wide range of perspectives on uncertainty, many of the contributors being the principal proponents in the controversy.Some of the notable issues which emerge from these papers revolve around an interval-based calculus of uncertainty, the Dempster-Shafer Theory, and probability as the best numeric model for uncertainty. There remain strong dissenting opinions not only about probability but even about the utility of any numeric method in this context.
[Ethics, empiricism and uncertainty].
Porz, R; Zimmermann, H; Exadaktylos, A K
2011-01-01
Accidents can lead to difficult boundary situations. Such situations often take place in the emergency units. The medical team thus often and inevitably faces professional uncertainty in their decision-making. It is essential to communicate these uncertainties within the medical team, instead of downplaying or overriding existential hurdles in decision-making. Acknowledging uncertainties might lead to alert and prudent decisions. Thus uncertainty can have ethical value in treatment or withdrawal of treatment. It does not need to be covered in evidence-based arguments, especially as some singular situations of individual tragedies cannot be grasped in terms of evidence-based medicine. © Georg Thieme Verlag KG Stuttgart · New York.
Uncertainty in hydrological signatures
McMillan, Hilary; Westerberg, Ida
2015-04-01
Information that summarises the hydrological behaviour or flow regime of a catchment is essential for comparing responses of different catchments to understand catchment organisation and similarity, and for many other modelling and water-management applications. Such information types derived as an index value from observed data are known as hydrological signatures, and can include descriptors of high flows (e.g. mean annual flood), low flows (e.g. mean annual low flow, recession shape), the flow variability, flow duration curve, and runoff ratio. Because the hydrological signatures are calculated from observed data such as rainfall and flow records, they are affected by uncertainty in those data. Subjective choices in the method used to calculate the signatures create a further source of uncertainty. Uncertainties in the signatures may affect our ability to compare different locations, to detect changes, or to compare future water resource management scenarios. The aim of this study was to contribute to the hydrological community's awareness and knowledge of data uncertainty in hydrological signatures, including typical sources, magnitude and methods for its assessment. We proposed a generally applicable method to calculate these uncertainties based on Monte Carlo sampling and demonstrated it for a variety of commonly used signatures. The study was made for two data rich catchments, the 50 km2 Mahurangi catchment in New Zealand and the 135 km2 Brue catchment in the UK. For rainfall data the uncertainty sources included point measurement uncertainty, the number of gauges used in calculation of the catchment spatial average, and uncertainties relating to lack of quality control. For flow data the uncertainty sources included uncertainties in stage/discharge measurement and in the approximation of the true stage-discharge relation by a rating curve. The resulting uncertainties were compared across the different signatures and catchments, to quantify uncertainty
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Multivariate residues and maximal unitarity
Søgaard, Mads; Zhang, Yang
2013-12-01
We extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number of fermions and scalars in the adjoint representation. Deca-cuts realized by replacement of real slice integration contours by higher-dimensional tori encircling the global poles are used to factorize the planar triple box onto a product of trees. We apply computational algebraic geometry and multivariate complex analysis to derive unique projectors for all master integral coefficients and obtain compact analytic formulae in terms of tree-level data.
Beeping a Maximal Independent Set
Afek, Yehuda; Alon, Noga; Bar-Joseph, Ziv; Cornejo, Alejandro; Haeupler, Bernhard; Kuhn, Fabian
2012-01-01
We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. At each time slot a node can either beep, that is, emit a signal, or be silent. At a particular time slot...
Maximal Congruences on Some Semigroups
Jintana Sanwong; R.P. Sullivan
2007-01-01
In 1976 Howie proved that a finite congruence-free semigroup is a simple group if it has at least three elements but no zero elementInfinite congruence-free semigroups are far more complicated to describe, but some have been constructed using semigroups of transformations (for example, by Howie in 1981 and by Marques in 1983)Here, forcertain semigroups S of numbers and of transformations, we determine all congruences p on S such that S/p is congruence-free, that is, we describe all maximal congruences on such semigroups S.
Nanosensing Backed by the Uncertainty Principle
I. Filikhin
2016-01-01
Full Text Available Possibility for a novel type of sensors for detecting nanosized substances (e.g., macromolecules or molecule clusters through their effects on electron tunneling in a double nanoscale semiconductor heterostructure is discussed. We studied spectral distributions of localized/delocalized states of a single electron in a double quantum well (DQW with relation to slight asymmetry perturbations. The asymmetry was modeled by modification of the dot shape and the confinement potential. Electron energy uncertainty is restricted by the differences between energy levels within the spectra of separated QWs. Hence, we established a direct relationship between the uncertainty of electron localization and the energy uncertainty. We have shown in various instances that a small violation of symmetry drastically affects the electron localization. These phenomena can be utilized to devise new sensing functionalities. The charge transport in such sensors is highly sensitive to minuscule symmetry violation caused by the detected substance. The detection of the electron localization constitutes the sensor signal.
Linear optics and quantum maps
Aiello, A; Woerdman, J P
2006-01-01
We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-\\emph{vs}-quantum formalism, we show how two-qubit maximally entangled mixed states (MEMS), can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion.
Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
Sailer, K; Nagy, S
2013-01-01
A projection method is proposed to treat the one-dimensional Schrodinger equation for a single particle when the Generalized Uncertainty Principle (GUP) generates an ultraviolet (UV) wavevector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited Quantum Mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the spreading time of a Gaussian wavepacket moving in free space. Indication is found that GUP accompanied by bandlimitation may cause departures of the low-lying energy levels of a particle in a box from those in ordinary Quantum Mechanics much less suppressed than commonly thought when GUP without bandlimitation is in work.
Knowledge discovery by accuracy maximization.
Cacciatore, Stefano; Luchinat, Claudio; Tenori, Leonardo
2014-04-01
Here we describe KODAMA (knowledge discovery by accuracy maximization), an unsupervised and semisupervised learning algorithm that performs feature extraction from noisy and high-dimensional data. Unlike other data mining methods, the peculiarity of KODAMA is that it is driven by an integrated procedure of cross-validation of the results. The discovery of a local manifold's topology is led by a classifier through a Monte Carlo procedure of maximization of cross-validated predictive accuracy. Briefly, our approach differs from previous methods in that it has an integrated procedure of validation of the results. In this way, the method ensures the highest robustness of the obtained solution. This robustness is demonstrated on experimental datasets of gene expression and metabolomics, where KODAMA compares favorably with other existing feature extraction methods. KODAMA is then applied to an astronomical dataset, revealing unexpected features. Interesting and not easily predictable features are also found in the analysis of the State of the Union speeches by American presidents: KODAMA reveals an abrupt linguistic transition sharply separating all post-Reagan from all pre-Reagan speeches. The transition occurs during Reagan's presidency and not from its beginning.
Inapproximability of maximal strip recovery
Jiang, Minghui
2009-01-01
In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \\msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \\ge 2$, a polynomial-time 2d-approximation for \\msr{d} was previously known. In this paper, we show that for any $d \\ge 2$, \\msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provi...
Maximal right smooth extension chains
Huang, Yun Bao
2010-01-01
If $w=u\\alpha$ for $\\alpha\\in \\Sigma=\\{1,2\\}$ and $u\\in \\Sigma^*$, then $w$ is said to be a \\textit{simple right extension}of $u$ and denoted by $u\\prec w$. Let $k$ be a positive integer and $P^k(\\epsilon)$ denote the set of all $C^\\infty$-words of height $k$. Set $u_{1},\\,u_{2},..., u_{m}\\in P^{k}(\\epsilon)$, if $u_{1}\\prec u_{2}\\prec ...\\prec u_{m}$ and there is no element $v$ of $P^{k}(\\epsilon)$ such that $v\\prec u_{1}\\text{or} u_{m}\\prec v$, then $u_{1}\\prec u_{2}\\prec...\\prec u_{m}$ is said to be a \\textit{maximal right smooth extension (MRSE) chains}of height $k$. In this paper, we show that \\textit{MRSE} chains of height $k$ constitutes a partition of smooth words of height $k$ and give the formula of the number of \\textit{MRSE} chains of height $k$ for each positive integer $k$. Moreover, since there exist the minimal height $h_1$ and maximal height $h_2$ of smooth words of length $n$ for each positive integer $n$, we find that \\textit{MRSE} chains of heights $h_1-1$ and $h_2+1$ are good candidates t...
Generalized uncertainty principles, effective Newton constant and regular black holes
Li, Xiang; Shen, You-Gen; Liu, Cheng-Zhou; He, Hong-Sheng; Xu, Lan-Fang
2016-01-01
In this paper, we explore the quantum spacetimes that are potentially connected with the generalized uncertainty principles. By analyzing the gravity-induced quantum interference pattern and the Gedanken for weighting photon, we find that the generalized uncertainty principles inspire the effective Newton constant as same as our previous proposal. A characteristic momentum associated with the tidal effect is suggested, which incorporates the quantum effect with the geometric nature of gravity. When the simplest generalized uncertainty principle is considered, the minimal model of the regular black holes is reproduced by the effective Newton constant. The black hole's tunneling probability, accurate to the second order correction, is carefully analyzed. We find that the tunneling probability is regularized by the size of the black hole remnant. Moreover, the black hole remnant is the final state of a tunneling process that the probability is minimized. A theory of modified gravity is suggested, by substituting...
Van Nooyen, R.R.P.; Hrachowitz, M.; Kolechkina, A.G.
2014-01-01
Even without uncertainty about the model structure or parameters, the output of a hydrological model run still contains several sources of uncertainty. These are: measurement errors affecting the input, the transition from continuous time and space to discrete time and space, which causes loss of in
Capel, H.W.; Cramer, J.S.; Estevez-Uscanga, O.
1995-01-01
'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medic
Guide for Uncertainty Communication
Wardekker, J.A.|info:eu-repo/dai/nl/306644398; Kloprogge, P.|info:eu-repo/dai/nl/306644312; Petersen, A.C.; Janssen, P.H.M.; van der Sluijs, J.P.|info:eu-repo/dai/nl/073427489
2013-01-01
Dealing with uncertainty, in terms of analysis and communication, is an important and distinct topic for PBL Netherlands Environmental Assessment Agency. Without paying adequate attention to the role and implications of uncertainty, research and assessment results may be of limited value and could
Computing with Epistemic Uncertainty
2015-01-01
modified the input uncertainties in any way. And by avoiding the need for simulation, various assumptions and selection of specific sampling...strategies that may affect results are also avoided . According with the Principle of Maximum Uncertainty , epistemic intervals represent the highest input...
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-12-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students (N=25) from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1) classical description, (2) mixed classical-quantum description, and (3) quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1) uncertainty as an extrinsic property of measurement, (2) uncertainty principle as measurement error or uncertainty, (3) uncertainty as measurement disturbance, and (4) uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction and the
Mengesha Ayene1
2011-11-01
Full Text Available Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students (N=25 from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1 classical description, (2 mixed classical-quantum description, and (3 quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1 uncertainty as an extrinsic property of measurement, (2 uncertainty principle as measurement error or uncertainty, (3 uncertainty as measurement disturbance, and (4 uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction
A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
Lomonaco, S J
2000-01-01
The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum mechanics and quantum computation, with enough material to begin reading the research literature in quantum computation and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000, and will appear in the AMS PSAPM volume entitled "Quantum Computation." Part 1 of the paper is an introduction the to the concept of the qubit. Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schrodinger's equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schrodinger picture, quantum entanglement, EPR paradox, quantum entropy. Part 3 gives a brief ...
Contraction coefficients for noisy quantum channels
Hiai, Fumio, E-mail: hiai.fumio@gmail.com [Tohoku University, Hakusan 3-8-16-303, Abiko 270-1154 (Japan); Ruskai, Mary Beth, E-mail: ruskai@member.ams.org [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2016-01-15
Generalized relative entropy, monotone Riemannian metrics, geodesic distance, and trace distance are all known to decrease under the action of quantum channels. We give some new bounds on, and relationships between, the maximal contraction for these quantities.
韩冰; 贺青; 李正坤; 李辰
2011-01-01
Based on the special structure of exciting coils system of Joule balance, the uncertainty sources of the magnetic density in the geometrical center of magnetic field was analysed and evaluated. The relative combined standard uncertainty of magnetic field in △H/H was 1.8 × 10 -3. In addition, it was proved that the largest components of uncertainty were due to terms with u ( I), which was 1.8 × 10-3 contribution to relative combined standard uncertainty in △H/H.Therefore the high-precision constant-current source was recommended to reduce uncertainty of magnetic field of Joule Balance.%基于焦耳天平激励线圈系统的具体结构,分析了磁场系统几何中心磁场强度的不确定度分量,磁场的相对合成标准不确定度ΔH/H达到1.8×10-3.证明了影响焦耳天平磁场最大的不确定度分量来源于线圈中加载电流的不确定度u(Ⅰ),它对磁场的相对合成标准不确定度ΔH/H影响达到1.8×10-3,因此推荐采用高稳定的恒流源来较少焦耳天平磁场的不确定度.
Liu Baoding [Tsinghua Univ., Beijing (China). Uncertainty Theory Lab.
2007-07-01
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, and countable subadditivity axioms. The goal of uncertainty theory is to study the behavior of uncertain phenomena such as fuzziness and randomness. The main topics include probability theory, credibility theory, and chance theory. For this new edition the entire text has been totally rewritten. More importantly, the chapters on chance theory and uncertainty theory are completely new. This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, and management science will find this work a stimulating and useful reference. (orig.)
Economic uncertainty and econophysics
Schinckus, Christophe
2009-10-01
The objective of this paper is to provide a methodological link between econophysics and economics. I will study a key notion of both fields: uncertainty and the ways of thinking about it developed by the two disciplines. After having presented the main economic theories of uncertainty (provided by Knight, Keynes and Hayek), I show how this notion is paradoxically excluded from the economic field. In economics, uncertainty is totally reduced by an a priori Gaussian framework-in contrast to econophysics, which does not use a priori models because it works directly on data. Uncertainty is then not shaped by a specific model, and is partially and temporally reduced as models improve. This way of thinking about uncertainty has echoes in the economic literature. By presenting econophysics as a Knightian method, and a complementary approach to a Hayekian framework, this paper shows that econophysics can be methodologically justified from an economic point of view.
Physical Uncertainty Bounds (PUB)
Vaughan, Diane Elizabeth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Preston, Dean L. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-19
This paper introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switching out the available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.
Measurement uncertainty and probability
Willink, Robin
2013-01-01
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
Optimal uncertainty relations in a modified Heisenberg algebra
Abdelkhalek, Kais; Fiedler, Leander; Mangano, Gianpiero; Schwonnek, René
2016-01-01
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations which are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min- and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min-entropy is exactly one bit.
Optimal uncertainty relations in a modified Heisenberg algebra
Abdelkhalek, Kais; Chemissany, Wissam; Fiedler, Leander; Mangano, Gianpiero; Schwonnek, René
2016-12-01
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.
Sciacchitano, Andrea; Wieneke, Bernhard
2016-08-01
This paper discusses the propagation of the instantaneous uncertainty of PIV measurements to statistical and instantaneous quantities of interest derived from the velocity field. The expression of the uncertainty of vorticity, velocity divergence, mean value and Reynolds stresses is derived. It is shown that the uncertainty of vorticity and velocity divergence requires the knowledge of the spatial correlation between the error of the x and y particle image displacement, which depends upon the measurement spatial resolution. The uncertainty of statistical quantities is often dominated by the random uncertainty due to the finite sample size and decreases with the square root of the effective number of independent samples. Monte Carlo simulations are conducted to assess the accuracy of the uncertainty propagation formulae. Furthermore, three experimental assessments are carried out. In the first experiment, a turntable is used to simulate a rigid rotation flow field. The estimated uncertainty of the vorticity is compared with the actual vorticity error root-mean-square, with differences between the two quantities within 5-10% for different interrogation window sizes and overlap factors. A turbulent jet flow is investigated in the second experimental assessment. The reference velocity, which is used to compute the reference value of the instantaneous flow properties of interest, is obtained with an auxiliary PIV system, which features a higher dynamic range than the measurement system. Finally, the uncertainty quantification of statistical quantities is assessed via PIV measurements in a cavity flow. The comparison between estimated uncertainty and actual error demonstrates the accuracy of the proposed uncertainty propagation methodology.
Relating quantum coherence and correlations with entropy-based measures.
Wang, Xiao-Li; Yue, Qiu-Ling; Yu, Chao-Hua; Gao, Fei; Qin, Su-Juan
2017-09-21
Quantum coherence and quantum correlations are important quantum resources for quantum computation and quantum information. In this paper, using entropy-based measures, we investigate the relationships between quantum correlated coherence, which is the coherence between subsystems, and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for all the maximally correlated states.
Generation of maximally entangled states of qudits using twin photons
Neves, L; Gómez, J G A; Monken, C H; Saavedra, C; Pádua, S; Neves, Leonardo
2004-01-01
We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin fotons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these differents paths. Experimental results for qudits with D=4 and D=8 are shown. We demonstrate that the generated states are entangled states.
Maximizing Information on the Environment by Dynamically Controlled Qubit Probes
Zwick, Analia; Álvarez, Gonzalo A.; Kurizki, Gershon
2016-01-01
We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to the quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic types of bath spectra, and the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.
Maximizing information on the environment by dynamically controlled qubit probes
Zwick, Analia; Kurizki, Gershon
2015-01-01
We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic bath spectra, the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.
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.
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
The maximal D = 4 supergravities
Wit, Bernard de [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Postbus 80.195, NL-3508 TD Utrecht (Netherlands); Samtleben, Henning [Laboratoire de Physique, ENS Lyon, 46 allee d' Italie, F-69364 Lyon CEDEX 07 (France); Trigiante, Mario [Dept. of Physics, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Turin (Italy)
2007-06-15
All maximal supergravities in four space-time dimensions are presented. The ungauged Lagrangians can be encoded in an E{sub 7(7)}-Sp(56; R)/GL(28) matrix associated with the freedom of performing electric/magnetic duality transformations. The gauging is defined in terms of an embedding tensor {theta} which encodes the subgroup of E{sub 7(7)} that is realized as a local invariance. This embedding tensor may imply the presence of magnetic charges which require corresponding dual gauge fields. The latter can be incorporated by using a recently proposed formulation that involves tensor gauge fields in the adjoint representation of E{sub 7(7)}. In this formulation the results take a universal form irrespective of the electric/magnetic duality basis. We present the general class of supersymmetric and gauge invariant Lagrangians and discuss a number of applications.
Maximizing profit using recommender systems
Das, Aparna; Ricketts, Daniel
2009-01-01
Traditional recommendation systems make recommendations based solely on the customer's past purchases, product ratings and demographic data without considering the profitability the items being recommended. In this work we study the question of how a vendor can directly incorporate the profitability of items into its recommender so as to maximize its expected profit while still providing accurate recommendations. Our approach uses the output of any traditional recommender system and adjust them according to item profitabilities. Our approach is parameterized so the vendor can control how much the recommendation incorporating profits can deviate from the traditional recommendation. We study our approach under two settings and show that it achieves approximately 22% more profit than traditional recommendations.
The maximal D=5 supergravities
de Wit, Bernard; Trigiante, M; Wit, Bernard de; Samtleben, Henning; Trigiante, Mario
2007-01-01
The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the \\bar{27} and tensor fields in the 27 representation of E_6. This novel tensor-vector system is subject to an intricate set of gauge transformations, describing 3(27-t) massless helicity degrees of freedom for the vector fields and 3t massive spin degrees of freedom for the tensor fields, where the (even) value of t depends on the gauging. The kinetic term of the tensor fields is accompanied by a unique Chern-Simons coupling which involves both vector and tensor fields. The Lagrangians are completely encoded in terms of the embedding tensor which defines the E_6 subgroup that is gauged by the vectors. The embedding tensor is subject to two constraints which ensure the consistency of the combined vector-tensor gauge transformations and the supersymmetry of the full Lagrangian. This new formulation encompasses all possible gaugings.
A Rational Decision Maker with Ordinal Utility under Uncertainty: Optimism and Pessimism
Han, Ji
2009-01-01
In game theory and artificial intelligence, decision making models often involve maximizing expected utility, which does not respect ordinal invariance. In this paper, the author discusses the possibility of preserving ordinal invariance and still making a rational decision under uncertainty.
Many Worlds, the Born Rule, and Self-Locating Uncertainty
Carroll, Sean M
2014-01-01
We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classical and quantum self-locating uncertainty, as in the cosmological multiverse.
Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations
Vasily E. Tarasov
2016-06-01
Full Text Available An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.
Braid group representation on quantum computation
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Background-independent quantization and the uncertainty principle
Hossain, Golam Mortuza; Husain, Viqar; Seahra, Sanjeev S, E-mail: ghossain@unb.c, E-mail: vhusain@unb.c, E-mail: sseahra@unb.c [Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3 (Canada)
2010-08-21
It is shown that polymer quantization leads to a modified uncertainty principle similar to that motivated by string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann-Robertson-Walker cosmology this translates to a scale factor dependence which gives a large effect in the early Universe.
Quantum-like Representation of Bayesian Updating
Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu; Khrennikov, Andrei; Basieva, Irina
2011-03-01
Recently, applications of quantum mechanics to coginitive psychology have been discussed, see [1]-[11]. It was known that statistical data obtained in some experiments of cognitive psychology cannot be described by classical probability model (Kolmogorov's model) [12]-[15]. Quantum probability is one of the most advanced mathematical models for non-classical probability. In the paper of [11], we proposed a quantum-like model describing decision-making process in a two-player game, where we used the generalized quantum formalism based on lifting of density operators [16]. In this paper, we discuss the quantum-like representation of Bayesian inference, which has been used to calculate probabilities for decision making under uncertainty. The uncertainty is described in the form of quantum superposition, and Bayesian updating is explained as a reduction of state by quantum measurement.
Quantum Interferometric Sensors
Kapale, K T; Lee, H; Kok, P; Dowling, J P; Kapale, Kishore T.; Didomenico, Leo D.; Lee, Hwang; Kok, Pieter; Dowling, Jonathan P.
2005-01-01
Quantum entanglement has the potential to revolutionize the entire field of interferometric sensing by providing many orders of magnitude improvement in interferometer sensitivity. The quantum-entangled particle interferometer approach is very general and applies to many types of interferometers. In particular, without nonlocal entanglement, a generic classical interferometer has a statistical-sampling shot-noise limited sensitivity that scales like $1/\\sqrt{N}$, where $N$ is the number of particles passing through the interferometer per unit time. However, if carefully prepared quantum correlations are engineered between the particles, then the interferometer sensitivity improves by a factor of $\\sqrt{N}$ to scale like 1/N, which is the limit imposed by the Heisenberg Uncertainty Principle. For optical interferometers operating at milliwatts of optical power, this quantum sensitivity boost corresponds to an eight-order-of-magnitude improvement of signal to noise. This effect can translate into a tremendous s...
Optimal Universal Uncertainty Relations
Li, Tao; Xiao, Yunlong; Ma, Teng; Fei, Shao-Ming; Jing, Naihuan; Li-Jost, Xianqing; Wang, Zhi-Xi
2016-01-01
We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002 (2013)]. The results give rise to state independent uncertainty relations satisfied by any nonnegative Schur-concave functions. On the other hand, a remarkable recent result of entropic uncertainty relation is the direct-sum majorization relation. In this paper, we illustrate our bounds by showing how they provide a complement to that in [Phys. Rev. A. 89, 052115 (2014)]. PMID:27775010
Subcycle quantum electrodynamics.
Riek, C; Sulzer, P; Seeger, M; Moskalenko, A S; Burkard, G; Seletskiy, D V; Leitenstorfer, A
2017-01-18
Squeezed states of electromagnetic radiation have quantum fluctuations below those of the vacuum field. They offer a unique resource for quantum information systems and precision metrology, including gravitational wave detectors, which require unprecedented sensitivity. Since the first experiments on this non-classical form of light, quantum analysis has been based on homodyning techniques and photon correlation measurements. These methods currently function in the visible to near-infrared and microwave spectral ranges. They require a well-defined carrier frequency, and photons contained in a quantum state need to be absorbed or amplified. Quantum non-demolition experiments may be performed to avoid the influence of a measurement in one quadrature, but this procedure comes at the expense of increased uncertainty in another quadrature. Here we generate mid-infrared time-locked patterns of squeezed vacuum noise. After propagation through free space, the quantum fluctuations of the electric field are studied in the time domain using electro-optic sampling with few-femtosecond laser pulses. We directly compare the local noise amplitude to that of bare (that is, unperturbed) vacuum. Our nonlinear approach operates off resonance and, unlike homodyning or photon correlation techniques, without absorption or amplification of the field that is investigated. We find subcycle intervals with noise levels that are substantially less than the amplitude of the vacuum field. As a consequence, there are enhanced fluctuations in adjacent time intervals, owing to Heisenberg's uncertainty principle, which indicate generation of highly correlated quantum radiation. Together with efforts in the far infrared, this work enables the study of elementary quantum dynamics of light and matter in an energy range at the boundary between vacuum and thermal background conditions.
Scaling and chiral extrapolation of pion mass and decay constant with maximally twisted mass QCD
Dimopoulos, P; Herdoiza, G; Jansen, K; Michael, C; Urbach, C
2008-01-01
We present an update of the results for pion mass and pion decay constant as obtained by the ETM collaboration in large scale simulations with maximally twisted mass fermions and two mass degenerate flavours of light quarks. We discuss the continuum, chiral and infinite volume extrapolation of these quantities as well as the extraction of low energy constants, and investigate possible systematic uncertainties.
Remote creation of quantum coherence
Ma, Teng; Zhao, Ming-Jing; Fei, Shao-Ming; Long, Gui-Lu
2016-10-01
We study remote creation of coherence (RCC) for a quantum system, A, with the help of quantum operations on another system, B, and one-way classical communication. We show that all the nonincoherent quantum states are useful for RCC and all the incoherent-quantum states are not. The necessary and sufficient conditions of RCC for the quantum operations on system B are presented for pure states. The upper bound of average RCC is derived, giving a relation among the entanglement (concurrence), the RCC of the given quantum state, and the RCC of the corresponding maximally entangled state. Moreover, for two-qubit systems we find a simple factorization law for the average remote-created coherence.
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...
Uncertainty, rationality, and agency
Hoek, Wiebe van der
2006-01-01
Goes across 'classical' borderlines of disciplinesUnifies logic, game theory, and epistemics and studies them in an agent-settingCombines classical and novel approaches to uncertainty, rationality, and agency
Introduction to uncertainty quantification
Sullivan, T J
2015-01-01
Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation, and numerous application areas in science and engineering. This text provides a framework in which the main objectives of the field of uncertainty quantification are defined, and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favourite problems to understand their strengths and weaknesses, also making the text suitable as a self-study. This text is designed as an introduction to uncertainty quantification for senior undergraduate and graduate students with a mathematical or statistical back...
Menger, Fredric M
2010-09-01
It might come as a disappointment to some chemists, but just as there are uncertainties in physics and mathematics, there are some chemistry questions we may never know the answer to either, suggests Fredric M. Menger.
EDITORIAL: Squeezed states and uncertainty relations
Jauregue-Renaud, Rocio; Kim, Young S.; Man'ko, Margarita A.; Moya-Cessa, Hector
2004-06-01
This special issue of Journal of Optics B: Quantum and Semiclassical Optics is composed mainly of extended versions of talks and papers presented at the Eighth International Conference on Squeezed States and Uncertainty Relations held in Puebla, Mexico on 9-13 June 2003. The Conference was hosted by Instituto de Astrofísica, Óptica y Electrónica, and the Universidad Nacional Autónoma de México. This series of meetings began at the University of Maryland, College Park, USA, in March 1991. The second and third workshops were organized by the Lebedev Physical Institute in Moscow, Russia, in 1992 and by the University of Maryland Baltimore County, USA, in 1993, respectively. Afterwards, it was decided that the workshop series should be held every two years. Thus the fourth meeting took place at the University of Shanxi in China and was supported by the International Union of Pure and Applied Physics (IUPAP). The next three meetings in 1997, 1999 and 2001 were held in Lake Balatonfüred, Hungary, in Naples, Italy, and in Boston, USA, respectively. All of them were sponsored by IUPAP. The ninth workshop will take place in Besançon, France, in 2005. The conference has now become one of the major international meetings on quantum optics and the foundations of quantum mechanics, where most of the active research groups throughout the world present their new results. Accordingly this conference has been able to align itself to the current trend in quantum optics and quantum mechanics. The Puebla meeting covered most extensively the following areas: quantum measurements, quantum computing and information theory, trapped atoms and degenerate gases, and the generation and characterization of quantum states of light. The meeting also covered squeeze-like transformations in areas other than quantum optics, such as atomic physics, nuclear physics, statistical physics and relativity, as well as optical devices. There were many new participants at this meeting, particularly
A linearization of quantum channels
Crowder, Tanner
2015-06-01
Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.
Lemaire, Maurice
2014-01-01
Science is a quest for certainty, but lack of certainty is the driving force behind all of its endeavors. This book, specifically, examines the uncertainty of technological and industrial science. Uncertainty and Mechanics studies the concepts of mechanical design in an uncertain setting and explains engineering techniques for inventing cost-effective products. Though it references practical applications, this is a book about ideas and potential advances in mechanical science.
Beeping a Maximal Independent Set
Afek, Yehuda; Bar-Joseph, Ziv; Cornejo, Alejandro; Haeupler, Bernhard; Kuhn, Fabian
2012-01-01
We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. At each time slot a node can either beep, that is, emit a signal, or be silent. At a particular time slot, beeping nodes receive no feedback, while silent nodes can only differentiate between none of its neighbors beeping, or at least one of its neighbors beeping. We start by proving a lower bound that shows that in this model, it is not possible to locally converge to an MIS in sub-polynomial time. We then study four different relaxations of the model which allow us to circumvent the lower bound and find an MIS in polylogarithmic time. First, we show that if a polynomial upper bound on the network size is known, it is possi...
Maximal switchability of centralized networks
Vakulenko, Sergei; Morozov, Ivan; Radulescu, Ovidiu
2016-08-01
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of N s weakly connected satellites, a property that we call n/N s -centrality. If the hub dynamics is slow, we obtain that the large time network dynamics is completely defined by the hub dynamics. Moreover, such networks are maximally flexible and switchable, in the sense that they can switch from a globally attractive rest state to any structurally stable dynamics when the response time of a special controller hub is changed. In particular, we show that a decrease of the controller hub response time can lead to a sharp variation in the network attractor structure: we can obtain a set of new local attractors, whose number can increase exponentially with N, the total number of nodes of the nework. These new attractors can be periodic or even chaotic. We provide an algorithm, which allows us to design networks with the desired switching properties, or to learn them from time series, by adjusting the interactions between hubs and satellites. Such switchable networks could be used as models for context dependent adaptation in functional genetics or as models for cognitive functions in neuroscience.
A Maximally Supersymmetric Kondo Model
Harrison, Sarah; Kachru, Shamit; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2012-02-17
We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N = 4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N = 4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial S3 in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.
Information Processing Structure of Quantum Gravity
Gyongyosi, Laszlo; Imre, Sandor
2014-05-01
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. Quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable. We provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We characterize the information transfer of the gravity space and the correlation measure functions of the gravity channel. We investigate the process of stimulated storage for quantum gravity memories, a phenomenon that exploits the information resource-pool property of quantum gravity. The results confirm that the benefits of the quantum gravity space can be exploited in quantum computations, particularly in the development of quantum computers. The results are supported by the grant COST Action MP1006.
Fractional revivals through Rényi uncertainty relations
Romera, E.; de Los Santos, F.
2008-07-01
We show that the Rényi uncertainty relations give a good description of the dynamical behavior of wave packets and constitute a sound approach to revival phenomena by analyzing three model systems: the simple harmonic oscillator, the infinite square well, and the quantum bouncer. We prove the usefulness of entropic uncertainty relations as a tool for identifying fractional revivals by providing a comparison in different contexts with the usual Heisenberg uncertainty relation and with the common approach in terms of the autocorrelation function.
Quantum mechanics the theoretical minimum
Susskind, Leonard
2014-01-01
From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Generalized uncertainty principles
Machluf, Ronny
2008-01-01
The phenomenon in the essence of classical uncertainty principles is well known since the thirties of the last century. We introduce a new phenomenon which is in the essence of a new notion that we introduce: "Generalized Uncertainty Principles". We show the relation between classical uncertainty principles and generalized uncertainty principles. We generalized "Landau-Pollak-Slepian" uncertainty principle. Our generalization relates the following two quantities and two scaling parameters: 1) The weighted time spreading $\\int_{-\\infty}^\\infty |f(x)|^2w_1(x)dx$, ($w_1(x)$ is a non-negative function). 2) The weighted frequency spreading $\\int_{-\\infty}^\\infty |\\hat{f}(\\omega)|^2w_2(\\omega)d\\omega$. 3) The time weight scale $a$, ${w_1}_a(x)=w_1(xa^{-1})$ and 4) The frequency weight scale $b$, ${w_2}_b(\\omega)=w_2(\\omega b^{-1})$. "Generalized Uncertainty Principle" is an inequality that summarizes the constraints on the relations between the two spreading quantities and two scaling parameters. For any two reason...
Quantum probabilistic logic programming
Balu, Radhakrishnan
2015-05-01
We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.
Marine reserves with ecological uncertainty.
Grafton, R Quentin; Kompas, Tom; Lindenmayer, David
2005-09-01
To help manage the fluctuations inherent in fish populations scientists have argued for both an ecosystem approach to management and the greater use of marine reserves. Support for reserves includes empirical evidence that they can raise the spawning biomass and mean size of exploited populations, increase the abundance of species and, relative to reference sites, raise population density, biomass, fish size and diversity. By contrast, fishers often oppose the establishment and expansion of marine reserves and claim that reserves provide few, if any, economic payoffs. Using a stochastic optimal control model with two forms of ecological uncertainty we demonstrate that reserves create a resilience effect that allows for the population to recover faster, and can also raise the harvest immediately following a negative shock. The tradeoff of a larger reserve is a reduced harvest in the absence of a negative shock such that a reserve will never encompass the entire population if the goal is to maximize the economic returns from harvesting, and fishing is profitable. Under a wide range of parameter values with ecological uncertainty, and in the 'worst case' scenario for a reserve, we show that a marine reserve can increase the economic payoff to fishers even when the harvested population is not initially overexploited, harvesting is economically optimal and the population is persistent. Moreover, we show that the benefits of a reserve cannot be achieved by existing effort or output controls. Our results demonstrate that, in many cases, there is no tradeoff between the economic payoff of fishers and ecological benefits when a reserve is established at equal to, or less than, its optimum size.
Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum
Nozari, Kourosh; Balef, F Rezaee
2013-01-01
We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra $[x,p]=i\\hbar\\big(1-\\beta p+2\\beta^{2}p^{2}\\big)$, where $\\beta $ is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.
Distributed Quantum Computation over Noisy Channels
Ekert, A K; Macchiavello, C; Cirac, J I
1999-01-01
We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. We show that for a sufficiently large number of nodes maximally entangled states are always advantageous over independent computations in each node, even in the presence of noise during the computation process.
On the energy-time uncertainty principle A didactical note
Giribet, G
2005-01-01
This brief note has the didactical purpose of discussing the meaning of the uncertainty principle involving energy and time in quantum mechanics by means of a review of the seminal works on this subject. The importance of this topic is, indeed, frequently neglected in several textbooks on quantum mechanics. Then, these pages are addressed to students attenting to an undergraduate course on quantum theory; and the original aim is that of presenting a list of references of the points that take part in the principal discussions on the subject. Special attention is devoted to the discussion of the fallacies, which are certainly persistent in the didactical literature.
Complementarity and Entanglement in Quantum Information Theory
Tessier, T E
2004-01-01
The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control of ensembles with potential applications in the field of quantum computing. We show how this entanglement sharing behavior may be studied in increasingly complex systems of both theoretical and experimental significance and demonstrate that entanglement sharing, as well as other unique features of entanglement, e.g. the fact that maximal information about a multipartite quantum system does not necessarily entail maximal information about its component subsystems, may be understood as specific consequences of the phenomenon of complementarity extended to composite quantum systems. We also present a local hidden-variable model supplemented by an efficient amount of classical communication that reproduces the quantum-mechanical predictions for the entire class of Gottesman-Kni...
Canonical Quantum Teleportation of Two-Particle Arbitrary State
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.
Do the Uncertainty Relations Really have Crucial Signiﬁcances for Physics?
Dumitru S.
2010-10-01
Full Text Available It is proved the falsity of idea that the Uncertainty Relations (UR have crucial signif- icances for physics. Additionally one argues for the necesity of an UR-disconnected quantum philosophy.
Nonlinear Schrödinger equation from generalized exact uncertainty principle
Rudnicki, Łukasz
2016-09-01
Inspired by the generalized uncertainty principle, which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle approach by Hall and Reginatto (2002 J. Phys. A: Math. Gen. 35 3289), and obtain a (quasi)nonlinear Schrödinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or plane-wave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitationally induced minimal position uncertainty proportional to the Planck length. Quite surprisingly, our result successfully merges the core of classical physics with non-relativistic quantum mechanics in its extremal form. We predict that the commonly accepted phenomenon, namely a modification of a free-particle dispersion relation due to quantum gravity might not occur in reality.
Lateral Modes in Quantum Cascade Lasers
Gregory C. Dente
2016-03-01
Full Text Available We will examine the waveguide mode losses in ridge-guided quantum cascade lasers. Our analysis illustrates how the low-loss mode for broad-ridge quantum cascade lasers (QCLs can be a higher-order lateral waveguide mode that maximizes the feedback from the sloped ridge-wall regions. The results are in excellent agreement with the near- and far-field data taken on broad-ridge-guided quantum cascade lasers processed with sloped ridge walls.
Network planning under uncertainties
Ho, Kwok Shing; Cheung, Kwok Wai
2008-11-01
One of the main focuses for network planning is on the optimization of network resources required to build a network under certain traffic demand projection. Traditionally, the inputs to this type of network planning problems are treated as deterministic. In reality, the varying traffic requirements and fluctuations in network resources can cause uncertainties in the decision models. The failure to include the uncertainties in the network design process can severely affect the feasibility and economics of the network. Therefore, it is essential to find a solution that can be insensitive to the uncertain conditions during the network planning process. As early as in the 1960's, a network planning problem with varying traffic requirements over time had been studied. Up to now, this kind of network planning problems is still being active researched, especially for the VPN network design. Another kind of network planning problems under uncertainties that has been studied actively in the past decade addresses the fluctuations in network resources. One such hotly pursued research topic is survivable network planning. It considers the design of a network under uncertainties brought by the fluctuations in topology to meet the requirement that the network remains intact up to a certain number of faults occurring anywhere in the network. Recently, the authors proposed a new planning methodology called Generalized Survivable Network that tackles the network design problem under both varying traffic requirements and fluctuations of topology. Although all the above network planning problems handle various kinds of uncertainties, it is hard to find a generic framework under more general uncertainty conditions that allows a more systematic way to solve the problems. With a unified framework, the seemingly diverse models and algorithms can be intimately related and possibly more insights and improvements can be brought out for solving the problem. This motivates us to seek a
Maximal inequalities for demimartingales and their applications
WANG XueJun; HU ShuHe
2009-01-01
In this paper,we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides.The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob's type maximal inequality for demimartingales,strong laws of large numbers and growth rate for demimartingales and associated random variables.At last,we give an equivalent condition of uniform integrability for demisubmartingales.
Maximal inequalities for demimartingales and their applications
无
2009-01-01
In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides. The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob’s type maximal inequality for demimartingales, strong laws of large numbers and growth rate for demimartingales and associated random variables. At last, we give an equivalent condition of uniform integrability for demisubmartingales.
Market uncertainty; Markedsusikkerhet
Doorman, Gerard; Holtan, Jon Anders; Mo, Birger; Groenli, Helle; Haaland, Magnar; Grinden, Bjoern
1997-04-10
In Norway, the project ``Market uncertainty`` has been in progress for over two years and resulted in increased skill in the use of the Grid System Operation Model. This report classifies some of the factors which lead to uncertainties in the electric power market. It has been examined whether these factors should be, or can be, modelled in the available simulation models. Some of the factors have been further considered and methods of modelling the associated uncertainties have been examined. It is concluded that (1) There is a need for automatic simulation of several scenarios in the model, and these scenarios should incorporate probability parameters, (2) At first it is most important that one can handle uncertainties in fuel prices and demand, (3) Market uncertainty which is due to irrational behaviour should be dealt with in a separate model. The difference between real and simulated prices should be analysed and modelled with a time series model, (4) Risk should be included in the Vansimtap model by way of feedback from simulations, (5) The marginal values of stored water as calculated by means of the various methods in use should be compared systematically. 9 refs., 16 figs., 5 tabs.
Interpreting uncertainty terms.
Holtgraves, Thomas
2014-08-01
Uncertainty terms (e.g., some, possible, good, etc.) are words that do not have a fixed referent and hence are relatively ambiguous. A model is proposed that specifies how, from the hearer's perspective, recognition of facework as a potential motive for the use of an uncertainty term results in a calibration of the intended meaning of that term. Four experiments are reported that examine the impact of face threat, and the variables that affect it (e.g., power), on the manner in which a variety of uncertainty terms (probability terms, quantifiers, frequency terms, etc.) are interpreted. Overall, the results demonstrate that increased face threat in a situation will result in a more negative interpretation of an utterance containing an uncertainty term. That the interpretation of so many different types of uncertainty terms is affected in the same way suggests the operation of a fundamental principle of language use, one with important implications for the communication of risk, subjective experience, and so on.
Investigation of Free Particle Propagator with Generalized Uncertainty Problem
Ghobakhloo, F
2016-01-01
We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of ordinary quantum mechanics is recovered for vanishing minimal length parameter.
Parameter Estimation, Model Reduction and Quantum Filtering
Chase, Bradley A
2009-01-01
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimator's uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.
Inflation in maximal gauged supergravities
Kodama, Hideo [Theory Center, KEK,Tsukuba 305-0801 (Japan); Department of Particles and Nuclear Physics,The Graduate University for Advanced Studies,Tsukuba 305-0801 (Japan); Nozawa, Masato [Dipartimento di Fisica, Università di Milano, and INFN, Sezione di Milano,Via Celoria 16, 20133 Milano (Italy)
2015-05-18
We discuss the dynamics of multiple scalar fields and the possibility of realistic inflation in the maximal gauged supergravity. In this paper, we address this problem in the framework of recently discovered 1-parameter deformation of SO(4,4) and SO(5,3) dyonic gaugings, for which the base point of the scalar manifold corresponds to an unstable de Sitter critical point. In the gauge-field frame where the embedding tensor takes the value in the sum of the 36 and 36’ representations of SL(8), we present a scheme that allows us to derive an analytic expression for the scalar potential. With the help of this formalism, we derive the full potential and gauge coupling functions in analytic forms for the SO(3)×SO(3)-invariant subsectors of SO(4,4) and SO(5,3) gaugings, and argue that there exist no new critical points in addition to those discovered so far. For the SO(4,4) gauging, we also study the behavior of 6-dimensional scalar fields in this sector near the Dall’Agata-Inverso de Sitter critical point at which the negative eigenvalue of the scalar mass square with the largest modulus goes to zero as the deformation parameter s approaches a critical value s{sub c}. We find that when the deformation parameter s is taken sufficiently close to the critical value, inflation lasts more than 60 e-folds even if the initial point of the inflaton allows an O(0.1) deviation in Planck units from the Dall’Agata-Inverso critical point. It turns out that the spectral index n{sub s} of the curvature perturbation at the time of the 60 e-folding number is always about 0.96 and within the 1σ range n{sub s}=0.9639±0.0047 obtained by Planck, irrespective of the value of the η parameter at the critical saddle point. The tensor-scalar ratio predicted by this model is around 10{sup −3} and is close to the value in the Starobinsky model.
Quantum logic networks for probabilistic teleportation
刘金明; 张永生; 郭光灿
2003-01-01
By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neuman measurement and classically controlled operations, we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit, atwo-particle entangled state, and an N-particle entanglement. Based on the quantum networks, we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
Quantum logic networks for probabilistic teleportation
刘金明; 张永生; 等
2003-01-01
By eans of the primitive operations consisting of single-qubit gates.two-qubit controlled-not gates,Von Neuman measurement and classically controlled operations.,we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit,a two-particle entangled state,and an N-particle entanglement.Based on the quantum networks,we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
Inequalities for quantum skew information
Audenaert, Koenraad; Cai, Liang; Hansen, Frank
2008-01-01
We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order...... relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information...... with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations....
A review of the generalized uncertainty principle.
Tawfik, Abdel Nasser; Diab, Abdel Magied
2015-12-01
Based on string theory, black hole physics, doubly special relativity and some 'thought' experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified dispersion relation, the space noncommutativity, the Lorentz invariance violation, and the quantum-gravity-induced birefringence effects are summarized. The origin of minimal measurable quantities and the different GUP approaches are reviewed and the corresponding observations are analysed. Bounds on the GUP parameter are discussed and implemented in the understanding of recent PLANCK observations of cosmic inflation. The higher-order GUP approaches predict minimal length uncertainty with and without maximum momenta. Possible arguments against the GUP are discussed; for instance, the concern about its compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action are addressed.
Revised Definitions of Quantum Dissonance and Quantum Discord
Zhang, Zhan-jun
2010-01-01
We show that all the correlations defined by K. Modi et al [Phys. Rev. Lett. {\\bf 104}, 080501 (2010)] except for the total mutual information should be redefined so that some physical quantities (e.g., the accessible maximal classical correlation and the resultant exact quantum discord) are right.
Measurement uncertainty relations
Busch, Paul, E-mail: paul.busch@york.ac.uk [Department of Mathematics, University of York, York (United Kingdom); Lahti, Pekka, E-mail: pekka.lahti@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Werner, Reinhard F., E-mail: reinhard.werner@itp.uni-hannover.de [Institut für Theoretische Physik, Leibniz Universität, Hannover (Germany)
2014-04-15
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order α rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.
Sustainability and uncertainty
Jensen, Karsten Klint
2007-01-01
and infers prescriptions from this requirement. These two approaches may conflict, and in this conflict the top-down approach has the upper hand, ethically speaking. However, the implicit goal in the top-down approach of justice between generations needs to be refined in several dimensions. But even given...... a clarified ethical goal, disagreements can arise. At present we do not know what substitutions will be possible in the future. This uncertainty clearly affects the prescriptions that follow from the measure of sustainability. Consequently, decisions about how to make future agriculture sustainable...... are decisions under uncertainty. There might be different judgments on likelihoods; but even given some set of probabilities, there might be disagreement on the right level of precaution in face of the uncertainty....
SAGD optimization under uncertainty
Gossuin, J.; Naccache, P. [Schlumberger SIS, Abingdon (United Kingdom); Bailley, W.; Couet, B. [Schlumberger-Doll Research, Cambridge, MA, (United States)
2011-07-01
In the heavy oil industry, the steam assisted gravity drainage process is often used to enhance oil recovery but this is a costly method and ways to make it more efficient are needed. Multiple methods have been developed to optimize the SAGD process but none of them explicitly considered uncertainty. This paper presents an optimization method in the presence of reservoir uncertainty. This process was tested on an SAGD model where three equi-probable geological models are possible. Preparatory steps were first performed to identify key variables and the optimization model was then proposed. The method was shown to be successful in handling a significant number of uncertainties, optimizing the SAGD process and preventing premature steam channels that can choke production. The optimization method presented herein was successfully applied to an SAGD process and was shown to provide better strategies than sensitivity analysis while handling more complex problems.
Lorentz Invariance Violation and Generalized Uncertainty Principle
Tawfik, A; Ali, A Farag
2016-01-01
Recent approaches for quantum gravity are conjectured to give predictions for a minimum measurable length, a maximum observable momentum and an essential generalization for the Heisenberg uncertainty principle (GUP). The latter is based on a momentum-dependent modification in the standard dispersion relation and leads to Lorentz invariance violation (LIV). The main features of the controversial OPERA measurements on the faster-than-light muon neutrino anomaly are used to calculate the time of flight delays $\\Delta t$ and the relative change $\\Delta v$ in the speed of neutrino in dependence on the redshift $z$. The results are compared with the OPERA measurements. We find that the measurements are too large to be interpreted as LIV. Depending on the rest mass, the propagation of high-energy muon neutrino can be superluminal. The comparison with the ultra high energy cosmic rays seems to reveals an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly ...
Sensitivity and uncertainty analysis
Cacuci, Dan G; Navon, Ionel Michael
2005-01-01
As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable scientific tools. Sensitivity and Uncertainty Analysis. Volume I: Theory focused on the mathematical underpinnings of two important methods for such analyses: the Adjoint Sensitivity Analysis Procedure and the Global Adjoint Sensitivity Analysis Procedure. This volume concentrates on the practical aspects of performing these analyses for large-scale systems. The applications addressed include two-phase flow problems, a radiative c
Uncertainty in artificial intelligence
Levitt, TS; Lemmer, JF; Shachter, RD
1990-01-01
Clearly illustrated in this volume is the current relationship between Uncertainty and AI.It has been said that research in AI revolves around five basic questions asked relative to some particular domain: What knowledge is required? How can this knowledge be acquired? How can it be represented in a system? How should this knowledge be manipulated in order to provide intelligent behavior? How can the behavior be explained? In this volume, all of these questions are addressed. From the perspective of the relationship of uncertainty to the basic questions of AI, the book divides naturally i
Orbital State Uncertainty Realism
Horwood, J.; Poore, A. B.
2012-09-01
Fundamental to the success of the space situational awareness (SSA) mission is the rigorous inclusion of uncertainty in the space surveillance network. The *proper characterization of uncertainty* in the orbital state of a space object is a common requirement to many SSA functions including tracking and data association, resolution of uncorrelated tracks (UCTs), conjunction analysis and probability of collision, sensor resource management, and anomaly detection. While tracking environments, such as air and missile defense, make extensive use of Gaussian and local linearity assumptions within algorithms for uncertainty management, space surveillance is inherently different due to long time gaps between updates, high misdetection rates, nonlinear and non-conservative dynamics, and non-Gaussian phenomena. The latter implies that "covariance realism" is not always sufficient. SSA also requires "uncertainty realism"; the proper characterization of both the state and covariance and all non-zero higher-order cumulants. In other words, a proper characterization of a space object's full state *probability density function (PDF)* is required. In order to provide a more statistically rigorous treatment of uncertainty in the space surveillance tracking environment and to better support the aforementioned SSA functions, a new class of multivariate PDFs are formulated which more accurately characterize the uncertainty of a space object's state or orbit. The new distribution contains a parameter set controlling the higher-order cumulants which gives the level sets a distinctive "banana" or "boomerang" shape and degenerates to a Gaussian in a suitable limit. Using the new class of PDFs within the general Bayesian nonlinear filter, the resulting filter prediction step (i.e., uncertainty propagation) is shown to have the *same computational cost as the traditional unscented Kalman filter* with the former able to maintain a proper characterization of the uncertainty for up to *ten
Commonplaces and social uncertainty
Lassen, Inger
2008-01-01
an example of risk discourse in which the use of commonplaces seems to be a central feature (Myers 2004: 81). My analyses support earlier findings that commonplaces serve important interactional purposes (Barton 1999) and that they are used for mitigating disagreement, for closing topics and for facilitating...... risk discourse (Myers 2005; 2007). In additional, however, I argue that commonplaces are used to mitigate feelings of insecurity caused by uncertainty and to negotiate new codes of moral conduct. Keywords: uncertainty, commonplaces, risk discourse, focus groups, appraisal...
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...
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...
Computing Maximally Supersymmetric Scattering Amplitudes
Stankowicz, James Michael, Jr.
This dissertation reviews work in computing N = 4 super-Yang--Mills (sYM) and N = 8 maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetime dimensions in novel ways. After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples. In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneous cut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4. In Ch. 5, the three-loop four-point amplitude is presented in the d log representation and in the pure integrand representation. In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at
Quantum Cryptography in Spin Networks
DENG Hong-Liang; FANG Xi-Ming
2007-01-01
In this paper we propose a new scheme of long-distance quantum cryptography based on spin networks with qubits stored in electron spins of quantum dots. By conditional Faraday rotation, single photon polarization measurement, and quantum state transfer, maximal-entangled Bell states for quantum cryptography between two long-distance parties are created. Meanwhile, efficient quantum state transfer over arbitrary distances is obtained in a spin chain by a proper choice of coupling strengths and using spin memory technique improved. We also analyse the security of the scheme against the cloning-based attack which can be also implemented in spin network and discover that this spin network cloning coincides with the optimal fidelity achieved by an eavesdropper for entanglement-based cryptography.
Holographic Software for Quantum Networks
Jaffe, Arthur; Wozniakowski, Alex
2016-01-01
We introduce diagrammatic protocols and holographic software for quantum information. We give a dictionary to translate between diagrammatic protocols and the usual algebraic protocols. In particular we describe the intuitive diagrammatic protocol for teleportation. We introduce the string Fourier transform $\\mathfrak{F}_{s}$ in quantum information, which gives a topological quantum computer. We explain why the string Fourier transform maps the zero particle state to the multiple-qudit resource state, which maximizes the entanglement entropy. We give a protocol to construct this $n$-qudit resource state $|Max \\rangle$, which uses minimal cost. We study Pauli $X,Y,Z$ matrices, and their relation with diagrammatic protocols. This work provides bridges between the new theory of planar para algebras and quantum information, especially in questions involving communication in quantum networks.
Are all maximally entangled states pure?
Cavalcanti, D; Terra-Cunha, M O
2005-01-01
In this Letter we study if all maximally entangled states are pure through several entanglement monotones. Our conclusions allow us to generalize the idea of monogamy of entanglement. Then we propose a polygamy of entanglement, which express that if a general multipartite state is maximally entangled it is necessarily factorized by any other system.
Sampling and Representation Complexity of Revenue Maximization
Dughmi, Shaddin; Han, Li; Nisan, Noam
2014-01-01
We consider (approximate) revenue maximization in auctions where the distribution on input valuations is given via "black box" access to samples from the distribution. We observe that the number of samples required -- the sample complexity -- is tightly related to the representation complexity of an approximately revenue-maximizing auction. Our main results are upper bounds and an exponential lower bound on these complexities.
Lisonek, Petr
1996-01-01
our classifications confirmthe maximality of previously known sets, the results in E^7 and E^8are new. Their counterpart in dimension larger than 10is a set of unit vectors with only two values of inner products in the Lorentz space R^{d,1}.The maximality of this set again follows from a bound due...
An ethical justification of profit maximization
Koch, Carsten Allan
2010-01-01
In much of the literature on business ethics and corporate social responsibility, it is more or less taken for granted that attempts to maximize profits are inherently unethical. The purpose of this paper is to investigate whether an ethical argument can be given in support of profit maximizing b...
Alternative trailer configurations for maximizing payloads
Jason D. Thompson; Dana Mitchell; John Klepac
2017-01-01
In order for harvesting contractors to stay ahead of increasing costs, it is imperative that they employ all options to maximize productivity and efficiency. Transportation can account for half the cost to deliver wood to a mill. Contractors seek to maximize truck payload to increase productivity. The Forest Operations Research Unit, Southern Research Station, USDA...
Cohomology of Weakly Reducible Maximal Triangular Algebras
董浙; 鲁世杰
2000-01-01
In this paper, we introduce the concept of weakly reducible maximal triangular algebras φwhich form a large class of maximal triangular algebras. Let B be a weakly closed algebra containing 5φ, we prove that the cohomology spaces Hn(φ, B) (n≥1) are trivial.
Approaches to Learning to Control Dynamic Uncertainty
Magda Osman
2015-10-01
Full Text Available In dynamic environments, when faced with a choice of which learning strategy to adopt, do people choose to mostly explore (maximizing their long term gains or exploit (maximizing their short term gains? More to the point, how does this choice of learning strategy influence one’s later ability to control the environment? In the present study, we explore whether people’s self-reported learning strategies and levels of arousal (i.e., surprise, stress correspond to performance measures of controlling a Highly Uncertain or Moderately Uncertain dynamic environment. Generally, self-reports suggest a preference for exploring the environment to begin with. After which, those in the Highly Uncertain environment generally indicated they exploited more than those in the Moderately Uncertain environment; this difference did not impact on performance on later tests of people’s ability to control the dynamic environment. Levels of arousal were also differentially associated with the uncertainty of the environment. Going beyond behavioral data, our model of dynamic decision-making revealed that, in actual fact, there was no difference in exploitation levels between those in the highly uncertain or moderately uncertain environments, but there were differences based on sensitivity to negative reinforcement. We consider the implications of our findings with respect to learning and strategic approaches to controlling dynamic uncertainty.
Bialynicki-Birula, I; Cirone, M.A.; Dahl, Jens Peder
2002-01-01
) a singular quantum force located at the origin, and (iii) the centrifugal force associated with non-vanishing angular momentum. Moreover, we use Heisenberg's uncertainty relation to introduce a lower bound for the kinetic energy of an ensemble of neutral particles. This bound is quadratic in the number......We present Heisenberg's equation of motion for the radial variable of a free non-relativistic particle in D dimensions. The resulting radial force consists of three contributions: (i) the quantum fictitious force which is either attractive or repulsive depending on the number of dimensions, (ii...... of atoms and can be traced back to the repulsive quantum fictitious potential. All three forces arise for a free particle: "Force without force"....
Bialynicki-Birula, I; Cirone, M.A.; Dahl, Jens Peder
2002-01-01
We present Heisenberg's equation of motion for the radial variable of a free non-relativistic particle in D dimensions. The resulting radial force consists of three contributions: (i) the quantum fictitious force which is either attractive or repulsive depending on the number of dimensions, (ii......) a singular quantum force located at the origin, and (iii) the centrifugal force associated with non-vanishing angular momentum. Moreover, we use Heisenberg's uncertainty relation to introduce a lower bound for the kinetic energy of an ensemble of neutral particles. This bound is quadratic in the number...... of atoms and can be traced back to the repulsive quantum fictitious potential. All three forces arise for a free particle: "Force without force"....
Valentini, Antony
2010-01-01
At the 1927 Solvay conference, three different theories of quantum mechanics were presented; however, the physicists present failed to reach a consensus. Today, many fundamental questions about quantum physics remain unanswered. One of the theories presented at the conference was Louis de Broglie's pilot-wave dynamics. This work was subsequently neglected in historical accounts; however, recent studies of de Broglie's original idea have rediscovered a powerful and original theory. In de Broglie's theory, quantum theory emerges as a special subset of a wider physics, which allows non-local signals and violation of the uncertainty principle. Experimental evidence for this new physics might be found in the cosmological-microwave-background anisotropies and with the detection of relic particles with exotic new properties predicted by the theory.
Bialynicki-Birula, I. [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Abt. fuer Quantenphysik, Univ. Ulm, Ulm (Germany); Cirone, M.A.; Straub, F.; Schleich, W.P. [Abt. fuer Quantenphysik, Univ. Ulm, Ulm (Germany); Dahl, J.P. [Abt. fuer Quantenphysik, Univ. Ulm, Ulm (Germany); Chemical Physics, Dept. of Chemistry, Technical Univ. of Denmark, Lyngby (Denmark); Seligman, T.H. [Centro de Ciencias Fisicas, Univ. of Mexico (UNAM), Cuernavaca (Mexico)
2002-07-01
We present Heisenberg's equation of motion for the radial variable of a free non-relativistic particle in D dimensions. The resulting radial force consists of three contributions: (i) the quantum fictitious force which is either attractive or repulsive depending on the number of dimensions, (ii) a singular quantum force located at the origin, and (iii) the centrifugal force associated with non-vanishing angular momentum. Moreover, we use Heisenberg's uncertainty relation to introduce a lower bound for the kinetic energy of an ensemble of neutral particles. This bound is quadratic in the number of atoms and can be traced back to the repulsive quantum fictitious potential. All three forces arise for a free particle: ''Force without force''. (orig.)
Inclusive fitness maximization: An axiomatic approach.
Okasha, Samir; Weymark, John A; Bossert, Walter
2014-06-07
Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it. Copyright © 2014 Elsevier Ltd. All rights reserved.
Maximal Hypersurfaces in Spacetimes with Translational Symmetry
Bulawa, Andrew
2016-01-01
We consider four-dimensional vacuum spacetimes which admit a free isometric spacelike R-action. Taking a quotient with respect to the R-action produces a three-dimensional quotient spacetime. We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in quotient spacetimes. First, we show that complete noncompact maximal hypersurfaces must either be flat cylinders S^1 x R or conformal to the Euclidean plane. Second, we establish a positive mass theorem for certain maximal hypersurfaces. Finally, while it is meaningful to use a bounded lapse when adopting the maximal hypersurface gauge condition in the four-dimensional (asymptotically flat) setting, it is shown here that nontrivial quotient spacetimes admit the maximal hypersurface gauge only with an unbounded lapse.
Coulson-Thomas, Colin
2015-01-01
Examines risk management and contemporary issues concerning risk governance from a board perspective, including risk tolerance, innovation, insurance, balancing risks and other factors, risk and strategies of diversification or focus, increasing flexibility to cope with uncertainty, periodic planning versus intelligent steering, and limiting downside risks and adverse consequences.
Uncertainties in repository modeling
Wilson, J.R.
1996-12-31
The distant future is ver difficult to predict. Unfortunately, our regulators are being enchouraged to extend ther regulatory period form the standard 10,000 years to 1 million years. Such overconfidence is not justified due to uncertainties in dating, calibration, and modeling.
Vehicle Routing under Uncertainty
Máhr, T.
2011-01-01
In this thesis, the main focus is on the study of a real-world transportation problem with uncertainties, and on the comparison of a centralized and a distributed solution approach in the context of this problem. We formalize the real-world problem, and provide a general framework to extend it with
Greasley, David; Madsen, Jakob B.
2006-01-01
A severe collapse of fixed capital formation distinguished the onset of the Great Depression from other investment downturns between the world wars. Using a model estimated for the years 1890-2000, we show that the expected profitability of capital measured by Tobin's q, and the uncertainty surro...... of the depression: rather, its slump helped to propel the wider collapse...
Cettolin, E.; Riedl, A.M.
2013-01-01
An important element for the public support of policies is their perceived justice. At the same time most policy choices have uncertain outcomes. We report the results of a first experiment investigating just allocations of resources when some recipients are exposed to uncertainty. Although, under c
范梦璇
2015-01-01
<正>Employ change-related uncertainty is a condition that under current continually changing business environment,the organizations also have to change,the change include strategic direction,structure and staffing levels to help company to keep competitive(Armenakis&Bedeian,1999);However;these
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.
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-01-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students' depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an…
Bose, Arko
2010-01-01
The suspicion that the existence of a minimal uncertainty in position measurements violates Lorentz invariance seems unfounded. It is shown that the existence of such a nonzero minimal uncertainty in position is not only consistent with Lorentz invariance, but that the latter also fixes the algebra between position and momentum which gives rise to this minimal uncertainty. We also investigate how this algebra affects the underlying quantum mechanical structure, and why, at the Planck scale, space can no longer be considered homogeneous.
2008-10-31
of the Apalachicola River drainage. Although this proposed division in classification appears to be generally accepted by the herpetological community...breeding in small forest ponds. Herpetological Review 33(4):275-280. Carle, F. L. and M. R. Strub. 1978. A new method for estimating population size...gopher frogs (Rana capito) and southern leopard frogs (Rana sphenocephala). Journal of Herpetology 42: 97-103. Grevstad, F.S. 2005. Simulating
Overcoming Registration Uncertainty in Image Super-Resolution: Maximize or Marginalize?
Andrew Zisserman
2007-01-01
Full Text Available In multiple-image super-resolution, a high-resolution image is estimated from a number of lower-resolution images. This usually involves computing the parameters of a generative imaging model (such as geometric and photometric registration, and blur and obtaining a MAP estimate by minimizing a cost function including an appropriate prior. Two alternative approaches are examined. First, both registrations and the super-resolution image are found simultaneously using a joint MAP optimization. Second, we perform Bayesian integration over the unknown image registration parameters, deriving a cost function whose only variables of interest are the pixel values of the super-resolution image. We also introduce a scheme to learn the parameters of the image prior as part of the super-resolution algorithm. We show examples on a number of real sequences including multiple stills, digital video, and DVDs of movies.
Quantum tunneling from the charged non-rotating BTZ black hole with GUP
Sadeghi, Jafar; Reza Shajiee, Vahid
2017-03-01
In the present paper, the quantum corrections to the temperature, entropy and specific heat capacity of the charged non-rotating BTZ black hole are studied by the generalized uncertainty principle in the tunneling formalism. It is shown that quantum corrected entropy would be of the form of predicted entropy in quantum gravity theories like string theory and loop quantum gravity.
On the Capability of Measurement-Based Quantum Feedback
Qi, Bo; Guo, Lei
2010-01-01
As a key method in dealing with uncertainties, feedback has been understood fairly well in classical control theory. But for quantum control systems, the capability of measurement-based feedback control (MFC) has not been investigated systematically. In contrast to the control of classical systems where the measurement effect is negligible, the quantum measurement will cause a quantum state to collapse, which will inevitably introduce additional uncertainties besides the system initial uncertainty. Therefore, there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement, and thus a theoretical investigation of the capability of MFC is of fundamental importance. In this paper, inspired by both the Heisenberg uncertainty principle for quantum systems and the investigation of the feedback capability for classical systems, we try to answer the following three basic questions: (i) How to choose the measurement channel appropriately? (ii) Is the MFC still superior ...
Experimental quantum measurement with a few photons
Rozema, Lee Arthur
This thesis presents the results of a series of four photonic experiments on the topic of quantum measurement. The first two experiments relate to quantum metrology, and the use of quantum states to increase the precision of measurements beyond what is possible with classical systems; first to detect and characterize decoherence, and then in the context of quantum imaging. The third experiment studies a fundamental question in quantum mechanics: "How much must a quantum system be disturbed by a measurement?". We use weak measurement to confirm a recent theoretical result, showing that if a particle's state is already sufficiently uncertain we can perform a measurement with very little disturbance -- contrary to common explanations of Heisenberg's uncertainty principle. The fourth experiment falls in the category of quantum computation. In quantum mechanics having multiple copies of an identical system allows us to extract more information than we can extract from a single copy (since quantum mechanics allows each system to be measured only once before collapsing). We present and experimentally implement a quantum algorithm to compress all of the "extractable information" present in an ensemble of identical copies of quantum bits into exponentially fewer quantum bits. The research presented here samples from a variety of topics in quantum information, showing in several contexts how fascinating quantum effects can be exploited to gain a "quantum enhancement". To enable these experiments two sources of entangled photons were built, and "hybrid" quantum systems (encoding information in multiple degrees of freedom of a photon) were used to implement quantum circuits. This thesis will present the details of one of these sources (a novel and practical source of entangled N00N states), which was used in a four-photon quantum metrology experiment. The other, more standard, source of polarization-entangled photon pairs will only briefly be reviewed to leave room for the
Outage Constrained Secrecy Rate Maximization Using Cooperative Jamming
Luo, Shuangyu; Petropulu, Athina
2012-01-01
We consider a Gaussian MISO wiretap channel, where a multi-antenna source communicates with a single-antenna destination in the presence of a single-antenna eavesdropper. The communication is assisted by multi-antenna helpers that act as jammers to the eavesdropper. Each helper independently transmits noise which lies in the null space of the channel to the destination, thus creates no interference to the destination. Under the assumption that there is eavesdropper channel uncertainty, we derive the optimal covariance matrix for the source signal so that the secrecy rate is maximized subject to probability of outage and power constraints. Assuming that the eavesdropper channels follow zero-mean Gaussian model with known covariances, we derive the outage probability in a closed form. Simulation results in support of the analysis are provided.
Managing Uncertainty for an Integrated Fishery
MB Hasan
2012-06-01
Full Text Available This paper investigates ways to deal with the uncertainties in fishing trawler scheduling and production planning in a quota-based integrated commercial fishery. A commercial fishery faces uncertainty mainly from variation in catch rate, which may be due to weather, and other environmental factors. The firm tries to manage this uncertainty through planning co-ordination of fishing trawler scheduling, catch quota, processing and labour allocation, and inventory control. Scheduling must necessarily be done over some finite planning horizon, and the trawler schedule itself introduces man-made variability, which in turn induces inventory in the processing plant. This induced inventory must be managed, complicated by the inability to plan easily beyond the current planning horizon. We develop a surprisingly simple innovation in inventory, which we have not seen in other papers on production management, which of requiring beginning inventory to equal ending inventory. This tool gives management a way to calculate a profit-maximizing safety stock that counter-acts the man-made variability due to the trawler scheduling. We found that the variability of catch rate had virtually no effects on the profitability with inventory. We report numerical results for several planning horizon models, based on data for a major New Zealand fishery.
Are all maximally entangled states pure?
Cavalcanti, D.; Brandão, F. G. S. L.; Terra Cunha, M. O.
2005-10-01
We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of the monogamy of entanglement: we establish the polygamy of entanglement, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.
An ethical justification of profit maximization
Koch, Carsten Allan
2010-01-01
In much of the literature on business ethics and corporate social responsibility, it is more or less taken for granted that attempts to maximize profits are inherently unethical. The purpose of this paper is to investigate whether an ethical argument can be given in support of profit maximizing...... behaviour. It is argued that some form of consequential ethics must be applied, and that both profit seeking and profit maximization can be defended from a rule-consequential point of view. It is noted, however, that the result does not apply unconditionally, but requires that certain form of profit (and...
Maximizing Statistical Power When Verifying Probabilistic Forecasts of Hydrometeorological Events
DeChant, C. M.; Moradkhani, H.
2014-12-01
Hydrometeorological events (i.e. floods, droughts, precipitation) are increasingly being forecasted probabilistically, owing to the uncertainties in the underlying causes of the phenomenon. In these forecasts, the probability of the event, over some lead time, is estimated based on some model simulations or predictive indicators. By issuing probabilistic forecasts, agencies may communicate the uncertainty in the event occurring. Assuming that the assigned probability of the event is correct, which is referred to as a reliable forecast, the end user may perform some risk management based on the potential damages resulting from the event. Alternatively, an unreliable forecast may give false impressions of the actual risk, leading to improper decision making when protecting resources from extreme events. Due to this requisite for reliable forecasts to perform effective risk management, this study takes a renewed look at reliability assessment in event forecasts. Illustrative experiments will be presented, showing deficiencies in the commonly available approaches (Brier Score, Reliability Diagram). Overall, it is shown that the conventional reliability assessment techniques do not maximize the ability to distinguish between a reliable and unreliable forecast. In this regard, a theoretical formulation of the probabilistic event forecast verification framework will be presented. From this analysis, hypothesis testing with the Poisson-Binomial distribution is the most exact model available for the verification framework, and therefore maximizes one's ability to distinguish between a reliable and unreliable forecast. Application of this verification system was also examined within a real forecasting case study, highlighting the additional statistical power provided with the use of the Poisson-Binomial distribution.
Traceability and Measurement Uncertainty
Tosello, Guido; De Chiffre, Leonardo
2004-01-01
respects necessary scientific precision and problem-solving approach of the field of engineering studies. Competences should be presented in a way that is methodologically and didactically optimised for employees with a mostly work-based vocational qualification and should at the same time be appealing...... and motivating to this important group. The developed e-learning system consists on 12 different chapters dealing with the following topics: 1. Basics 2. Traceability and measurement uncertainty 3. Coordinate metrology 4. Form measurement 5. Surface testing 6. Optical measurement and testing 7. Measuring rooms 8....... Machine tool testing 9. The role of manufacturing metrology for QM 10. Inspection planning 11. Quality management of measurements incl. Documentation 12. Advanced manufacturing measurement technology The present report (which represents the section 2 - Traceability and Measurement Uncertainty – of the e...
Vámos, Tibor
The gist of the paper is the fundamental uncertain nature of all kinds of uncertainties and consequently a critical epistemic review of historical and recent approaches, computational methods, algorithms. The review follows the development of the notion from the beginnings of thinking, via the Aristotelian and Skeptic view, the medieval nominalism and the influential pioneering metaphors of ancient India and Persia to the birth of modern mathematical disciplinary reasoning. Discussing the models of uncertainty, e.g. the statistical, other physical and psychological background we reach a pragmatic model related estimation perspective, a balanced application orientation for different problem areas. Data mining, game theories and recent advances in approximation algorithms are discussed in this spirit of modest reasoning.
Designing lattice structures with maximal nearest-neighbor entanglement
Navarro-Munoz, J C; Lopez-Sandoval, R [Instituto Potosino de Investigacion CientIfica y Tecnologica, Camino a la presa San Jose 2055, 78216 San Luis Potosi (Mexico); Garcia, M E [Theoretische Physik, FB 18, Universitaet Kassel and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), Heinrich-Plett-Str.40, 34132 Kassel (Germany)
2009-08-07
In this paper, we study the numerical optimization of nearest-neighbor concurrence of bipartite one- and two-dimensional lattices, as well as non-bipartite two-dimensional lattices. These systems are described in the framework of a tight-binding Hamiltonian while the optimization of concurrence was performed using genetic algorithms. Our results show that the concurrence of the optimized lattice structures is considerably higher than that of non-optimized systems. In the case of one-dimensional chains, the concurrence increases dramatically when the system begins to dimerize, i.e., it undergoes a structural phase transition (Peierls distortion). This result is consistent with the idea that entanglement is maximal or shows a singularity near quantum phase transitions. Moreover, the optimization of concurrence in two-dimensional bipartite and non-bipartite lattices is achieved when the structures break into smaller subsystems, which are arranged in geometrically distinguishable configurations.
Random graph states, maximal flow and Fuss-Catalan distributions
Collins, BenoIt; Nechita, Ion [Department of Mathematics and Statistics, University of Ottawa, Ontario K1N8M2 (Canada); Zyczkowski, Karol [Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland)
2010-07-09
For any graph consisting of k vertices and m edges we construct an ensemble of random pure quantum states which describe a system composed of 2m subsystems. Each edge of the graph represents a bipartite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated with a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze the statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.
Random graph states, maximal flow and Fuss-Catalan distributions
Collins, Benoit; Zyczkowski, Karol
2010-01-01
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated to a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by thes...
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
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.
Coalition Formation under Uncertainty
2010-03-01
Unfortunately, many current approaches to coalition formation lack provi- sions for uncertainty. This prevents application of coalition formation techniques ...should also include mechanisms and processing techniques that provide stabil- ity, scalability, and, at a minimum, optimality relative to agent beliefs...relocate a piano . For the sake of simplicity, assume payment is divided evenly among the participants in the move (i.e., each mover has the same utility or
Optimizing production under uncertainty
Rasmussen, Svend
This Working Paper derives criteria for optimal production under uncertainty based on the state-contingent approach (Chambers and Quiggin, 2000), and discusses po-tential problems involved in applying the state-contingent approach in a normative context. The analytical approach uses the concept o...... the relative benefits and of using the state-contingent approach in a norma-tive context, compared to the EV model....
Uncertainty in artificial intelligence
Shachter, RD; Henrion, M; Lemmer, JF
1990-01-01
This volume, like its predecessors, reflects the cutting edge of research on the automation of reasoning under uncertainty.A more pragmatic emphasis is evident, for although some papers address fundamental issues, the majority address practical issues. Topics include the relations between alternative formalisms (including possibilistic reasoning), Dempster-Shafer belief functions, non-monotonic reasoning, Bayesian and decision theoretic schemes, and new inference techniques for belief nets. New techniques are applied to important problems in medicine, vision, robotics, and natural language und
Aggregating and Communicating Uncertainty.
1980-04-01
means for identifying and communicating uncertainty. i 12- APPENDIX A BIBLIOGRAPHY j| 1. Ajzen , Icek ; "Intuitive Theories of Events and the Effects...disregarding valid but noncausal information." (Icak Ajzen , "Intuitive Theo- ries of Events and the Effects of Base-Rate Information on Prediction...9 4i,* ,4.. -. .- S % to the criterion while disregarding valid but noncausal information." (Icak Ajzen , "Intuitive Theories of Events and the Effects
1981-05-15
Variants of Uncertainty Daniel Kahneman University of British Columbia Amos Tversky Stanford University DTI-C &%E-IECTE ~JUNO 1i 19 8 1j May 15, 1981... Dennett , 1979) in which different parts have ac- cess to different data, assign then different weights and hold different views of the situation...2robable and t..h1 provable. Oxford- Claredor Press, 1977. Dennett , D.C. Brainstorms. Hassocks: Harvester, 1979. Donchin, E., Ritter, W. & McCallum, W.C
Relativistic quantum correlations in bipartite fermionic states
S KHAN; N A KHAN
2016-10-01
The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spincorrelations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the otherhand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Uncertainty Quantification in Aeroelasticity
Beran, Philip; Stanford, Bret; Schrock, Christopher
2017-01-01
Physical interactions between a fluid and structure, potentially manifested as self-sustained or divergent oscillations, can be sensitive to many parameters whose values are uncertain. Of interest here are aircraft aeroelastic interactions, which must be accounted for in aircraft certification and design. Deterministic prediction of these aeroelastic behaviors can be difficult owing to physical and computational complexity. New challenges are introduced when physical parameters and elements of the modeling process are uncertain. By viewing aeroelasticity through a nondeterministic prism, where key quantities are assumed stochastic, one may gain insights into how to reduce system uncertainty, increase system robustness, and maintain aeroelastic safety. This article reviews uncertainty quantification in aeroelasticity using traditional analytical techniques not reliant on computational fluid dynamics; compares and contrasts this work with emerging methods based on computational fluid dynamics, which target richer physics; and reviews the state of the art in aeroelastic optimization under uncertainty. Barriers to continued progress, for example, the so-called curse of dimensionality, are discussed.
Calibration Under Uncertainty.
Swiler, Laura Painton; Trucano, Timothy Guy
2005-03-01
This report is a white paper summarizing the literature and different approaches to the problem of calibrating computer model parameters in the face of model uncertainty. Model calibration is often formulated as finding the parameters that minimize the squared difference between the model-computed data (the predicted data) and the actual experimental data. This approach does not allow for explicit treatment of uncertainty or error in the model itself: the model is considered the %22true%22 deterministic representation of reality. While this approach does have utility, it is far from an accurate mathematical treatment of the true model calibration problem in which both the computed data and experimental data have error bars. This year, we examined methods to perform calibration accounting for the error in both the computer model and the data, as well as improving our understanding of its meaning for model predictability. We call this approach Calibration under Uncertainty (CUU). This talk presents our current thinking on CUU. We outline some current approaches in the literature, and discuss the Bayesian approach to CUU in detail.
Uncertainty quantified trait predictions
Fazayeli, Farideh; Kattge, Jens; Banerjee, Arindam; Schrodt, Franziska; Reich, Peter
2015-04-01
Functional traits of organisms are key to understanding and predicting biodiversity and ecological change, which motivates continuous collection of traits and their integration into global databases. Such composite trait matrices are inherently sparse, severely limiting their usefulness for further analyses. On the other hand, traits are characterized by the phylogenetic trait signal, trait-trait correlations and environmental constraints, all of which provide information that could be used to statistically fill gaps. We propose the application of probabilistic models which, for the first time, utilize all three characteristics to fill gaps in trait databases and predict trait values at larger spatial scales. For this purpose we introduce BHPMF, a hierarchical Bayesian extension of Probabilistic Matrix Factorization (PMF). PMF is a machine learning technique which exploits the correlation structure of sparse matrices to impute missing entries. BHPMF additionally utilizes the taxonomic hierarchy for trait prediction. Implemented in the context of a Gibbs Sampler MCMC approach BHPMF provides uncertainty estimates for each trait prediction. We present comprehensive experimental results on the problem of plant trait prediction using the largest database of plant traits, where BHPMF shows strong empirical performance in uncertainty quantified trait prediction, outperforming the state-of-the-art based on point estimates. Further, we show that BHPMF is more accurate when it is confident, whereas the error is high when the uncertainty is high.
Participation under Uncertainty
Boudourides, Moses A. [Univ. of Patras, Rio-Patras (Greece). Dept. of Mathematics
2003-10-01
This essay reviews a number of theoretical perspectives about uncertainty and participation in the present-day knowledge-based society. After discussing the on-going reconfigurations of science, technology and society, we examine how appropriate for policy studies are various theories of social complexity. Post-normal science is such an example of a complexity-motivated approach, which justifies civic participation as a policy response to an increasing uncertainty. But there are different categories and models of uncertainties implying a variety of configurations of policy processes. A particular role in all of them is played by expertise whose democratization is an often-claimed imperative nowadays. Moreover, we discuss how different participatory arrangements are shaped into instruments of policy-making and framing regulatory processes. As participation necessitates and triggers deliberation, we proceed to examine the role and the barriers of deliberativeness. Finally, we conclude by referring to some critical views about the ultimate assumptions of recent European policy frameworks and the conceptions of civic participation and politicization that they invoke.
Wang, Dong; Ming, Fei; Huang, Ai-Jun; Sun, Wen-Yang; Ye, Liu
2017-09-01
The uncertainty principle configures a low bound to the measuring precision for a pair of non-commuting observables, and hence is considerably nontrivial to quantum precision measurement in the field of quantum information theory. In this letter, we consider the entropic uncertainty relation (EUR) in the context of quantum memory in a two-qubit isotropic Heisenberg spin chain. Specifically, we explore the dynamics of EUR in a practical scenario, where two associated nodes of a one-dimensional XXX-spin chain, under an inhomogeneous magnetic field, are connected to a thermal entanglement. We show that the temperature and magnetic field effect can lead to the inflation of the measuring uncertainty, stemming from the reduction of systematic quantum correlation. Notably, we reveal that, firstly, the uncertainty is not fully dependent on the observed quantum correlation of the system; secondly, the dynamical behaviors of the measuring uncertainty are relatively distinct with respect to ferromagnetism and antiferromagnetism chains. Meanwhile, we deduce that the measuring uncertainty is dramatically correlated with the mixedness of the system, implying that smaller mixedness tends to reduce the uncertainty. Furthermore, we propose an effective strategy to control the uncertainty of interest by means of quantum weak measurement reversal. Therefore, our work may shed light on the dynamics of the measuring uncertainty in the Heisenberg spin chain, and thus be important to quantum precision measurement in various solid-state systems.
Fifth International Conference on Squeezed States and Uncertainty Relations
Han, D. (Editor); Janszky, J. (Editor); Kim, Y. S. (Editor); Man'ko, V. I. (Editor)
1998-01-01
The Fifth International Conference on Squeezed States and Uncertainty Relations was held at Balatonfured, Hungary, on 27-31 May 1997. This series was initiated in 1991 at the College Park Campus of the University of Maryland as the Workshop on Squeezed States and Uncertainty Relations. The scientific purpose of this series was to discuss squeezed states of light, but in recent years the scope is becoming broad enough to include studies of uncertainty relations and squeeze transformations in all branches of physics including quantum optics and foundations of quantum mechanics. Quantum optics will continue playing the pivotal role in the future, but the future meetings will include all branches of physics where squeeze transformations are basic. As the meeting attracted more participants and started covering more diversified subjects, the fourth meeting was called an international conference. The Fourth International Conference on Squeezed States and Uncertainty Relations was held in 1995 was hosted by Shanxi University in Taiyuan, China. The fifth meeting of this series, which was held at Balatonfured, Hungary, was also supported by the IUPAP. In 1999, the Sixth International Conference will be hosted by the University of Naples in 1999. The meeting will take place in Ravello near Naples.
Transition Path Time Distribution, Tunneling Times, Friction, and Uncertainty
Pollak, Eli
2017-02-01
A quantum mechanical transition path time probability distribution is formulated and its properties are studied using a parabolic barrier potential model. The average transit time is well defined and readily calculated. It is smaller than the analogous classical mechanical average transit time, vanishing at the crossover temperature. It provides a direct route for determining tunneling times. The average time may be also used to define a coarse grained momentum of the system for the passage from one side of the barrier to the other. The product of the uncertainty in this coarse grained momentum with the uncertainty in the location of the particle is shown under certain conditions to be smaller than the ℏ/2 formal uncertainty limit. The model is generalized to include friction in the form of a bilinear interaction with a harmonic bath. Using an Ohmic friction model one finds that increasing the friction, increases the transition time. Only moderate values of the reduced friction coefficient are needed for the quantum transition time and coarse grained uncertainty to approach the classical limit which is smaller than ℏ/2 when the friction is not too small. These results show how one obtains classical dynamics from a pure quantum system without invoking any further assumptions, approximations, or postulates.
A Criterion for Maximally Six-Qubit Entangled States via Coefficient Matrix
Yu, Yan; Zha, Xin Wei; Li, Wei
2017-03-01
In a recent paper (J. Phys. A: Math. Theor 45, 075308 (2012)), Li et al. established the coefficient matrix of six-qubit entangled states. With an emphasis on six qubits, we present a new criterion for maximally six-qubit entangled states via those coefficient matrices. By calculating the determinants of coefficient matrix, one use the criterion that characterize these states. Moreover, the criterion via the coefficient matrices gives rise to the combination of maximally multi-qubit entangled state(MMES) and matrix, and we believe that the new criterion can play an important role in quantum information.
On-demand source of maximally entangled photon pairs using the biexciton-exciton radiative cascade
Winik, R.; Cogan, D.; Don, Y.; Schwartz, I.; Gantz, L.; Schmidgall, E. R.; Livneh, N.; Rapaport, R.; Buks, E.; Gershoni, D.
2017-06-01
We perform full time-resolved tomographic measurements of the polarization state of pairs of photons emitted during the radiative cascade of the confined biexciton in a semiconductor quantum dot. The biexciton was deterministically initiated using a π -area pulse into the biexciton two-photon absorption resonance. Our measurements demonstrate that the polarization states of the emitted photon pair are maximally entangled. We show that the measured degree of entanglement depends solely on the temporal resolution by which the time difference between the emissions of the photon pair is determined. A route for fabricating an on-demand source of maximally polarization entangled photon pairs is thereby provided.
Experimental estimation of entanglement at the quantum limit.
Brida, Giorgio; Degiovanni, Ivo Pietro; Florio, Angela; Genovese, Marco; Giorda, Paolo; Meda, Alice; Paris, Matteo G A; Shurupov, Alexander
2010-03-12
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.
Information Processing Structure of Quantum Gravity
Gyongyosi, Laszlo
2014-01-01
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable. In this work, we provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We reveal that the quantum gravity space acts as a background noise on the local environment states. We characterize the properties of the noise of the quantum gravity space and show that it allows the separate local...
Scarani, Valerio; Iblisdir, Sofyan; Gisin, Nicolas; Acin, Antonio
2005-01-01
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional an...
HEALTH INSURANCE: CONTRIBUTIONS AND REIMBURSEMENT MAXIMAL
HR Division
2000-01-01
Affected by both the salary adjustment index on 1.1.2000 and the evolution of the staff members and fellows population, the average reference salary, which is used as an index for fixed contributions and reimbursement maximal, has changed significantly. An adjustment of the amounts of the reimbursement maximal and the fixed contributions is therefore necessary, as from 1 January 2000.Reimbursement maximalThe revised reimbursement maximal will appear on the leaflet summarising the benefits for the year 2000, which will soon be available from the divisional secretariats and from the AUSTRIA office at CERN.Fixed contributionsThe fixed contributions, applicable to some categories of voluntarily insured persons, are set as follows (amounts in CHF for monthly contributions):voluntarily insured member of the personnel, with complete coverage:815,- (was 803,- in 1999)voluntarily insured member of the personnel, with reduced coverage:407,- (was 402,- in 1999)voluntarily insured no longer dependent child:326,- (was 321...
Maximizing throughput by evaluating critical utilization paths
Weeda, P.J.
1991-01-01
Recently the relationship between batch structure, bottleneck machine and maximum throughput has been explored for serial, convergent and divergent process configurations consisting of two machines and three processes. In three of the seven possible configurations a multiple batch structure maximize
Relationship between maximal exercise parameters and individual ...
Relationship between maximal exercise parameters and individual time trial ... It is widely accepted that the ventilatory threshold (VT) is an important ... This study investigated whether the physiological responses during a 20km time trial (TT) ...
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Simple technique for maximal thoracic muscle harvest.
Marshall, M Blair; Kaiser, Larry R; Kucharczuk, John C
2004-04-01
We present a modification of technique for standard muscle flap harvest, the placement of cutaneous traction sutures. This technique allows for maximal dissection of the thoracic muscles even through minimal incisions. Through improved exposure and traction, complete dissection of the muscle bed can be performed and the tissue obtained maximized. Because more muscle bulk is obtained with this technique, the need for a second muscle may be prevented.
MAXIMAL POINTS OF A REGULAR TRUTH FUNCTION
Every canonical linearly separable truth function is a regular function, but not every regular truth function is linearly separable. The most...promising method of determining which of the regular truth functions are linearly separable r quires finding their maximal and minimal points. In this...report is developed a quick, systematic method of finding the maximal points of any regular truth function in terms of its arithmetic invariants. (Author)
Maximal Subgroups of Skew Linear Groups
M. Mahdavi-Hezavehi
2002-01-01
Let D be an infinite division algebra of finite dimension over its centre Z(D) = F, and n a positive integer. The structure of maximal subgroups of skew linear groups are investigated. In particular, assume N is a normal subgroup of GLn(D) and M is a maximal subgroup of N containing Z(N). It is shown that if M/Z(N) is finite, then N is central.
Additive Approximation Algorithms for Modularity Maximization
Kawase, Yasushi; Matsui, Tomomi; Miyauchi, Atsushi
2016-01-01
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find a partition $\\mathcal{C}$ of $V$ that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical approximation guarantee. Recently, to overcome this issue, the design of modularity max...
Uncertainty in magnetic activity indices
2008-01-01
Magnetic activity indices are widely used in theoretical studies of solar-terrestrial coupling and space weather prediction. However, the indices suffer from various uncertainties, which limit their application and even mislead to incorrect conclu-sion. In this paper we analyze three most popular indices, Kp, AE and Dst. Three categories of uncertainties in magnetic indices are discussed: "data uncertainty" originating from inadequate data processing, "station uncertainty" caused by in-complete station covering, and "physical uncertainty" stemming from unclear physical mechanism. A comparison between magnetic disturbances and related indices indicate that the residual Sq will cause an uncertainty of 1―2 in K meas-urement, the uncertainty in saturated AE is as much as 50%, and the uncertainty in Dst index caused by the partial ring currents is about a half of the partial ring cur-rent.
Uncertainty in magnetic activity indices
XU WenYao
2008-01-01
Magnetic activity indices are widely used in theoretical studies of solar-terrestrial coupling and space weather prediction. However, the indices suffer from various uncertainties, which limit their application and even mislead to incorrect conclu-sion. In this paper we analyze three most popular indices, Kp, AE and Dst. Three categories of uncertainties in magnetic indices are discussed: "data uncertainty" originating from inadequate data processing, "station uncertainty" caused by in-complete station covering, and "physical uncertainty" stemming from unclear physical mechanism. A comparison between magnetic disturbances and related indices indicate that the residual Sq will cause an uncertainty of 1-2 in K meas-urement, the uncertainty in saturated AE is as much as 50%, and the uncertainty in Dst index caused by the partial ring currents is about a half of the partial ring cur-rent.
Quantum CPU and Quantum Algorithm
Wang, An Min
1999-01-01
Making use of an universal quantum network -- QCPU proposed by me\\upcite{My1}, it is obtained that the whole quantum network which can implement some the known quantum algorithms including Deutsch algorithm, quantum Fourier transformation, Shor's algorithm and Grover's algorithm.
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum Computer Games: Quantum Minesweeper
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Shields, William
2004-05-01
Karl Popper, though not trained as a physicist and embarrassed early in his career by a physics error pointed out by Einstein and Bohr, ultimately made substantial contributions to the interpretation of quantum mechanics. As was often the case, Popper initially formulated his position by criticizing the views of others - in this case Niels Bohr and Werner Heisenberg. Underlying Popper's criticism was his belief that, first, the "standard interpretation" of quantum mechanics, sometimes called the Copenhagen interpretation, abandoned scientific realism and second, the assertion that quantum theory was "complete" (an assertion rejected by Einstein among others) amounted to an unfalsifiable claim. Popper insisted that the most basic predictions of quantum mechanics should continue to be tested, with an eye towards falsification rather than mere adding of decimal places to confirmatory experiments. His persistent attacks on the Copenhagen interpretation were aimed not at the uncertainty principle itself and the formalism from which it was derived, but at the acceptance by physicists of an unclear epistemology and ontology that left critical questions unanswered. In 1999, physicists at the University of Maryland conducted a version of Popper's Experiment, re-igniting the debate over quantum predictions and the role of locality in physics.
Maximal Frequent Itemset Generation Using Segmentation Apporach
M.Rajalakshmi
2011-09-01
Full Text Available Finding frequent itemsets in a data source is a fundamental operation behind Association Rule Mining.Generally, many algorithms use either the bottom-up or top-down approaches for finding these frequentitemsets. When the length of frequent itemsets to be found is large, the traditional algorithms find all thefrequent itemsets from 1-length to n-length, which is a difficult process. This problem can be solved bymining only the Maximal Frequent Itemsets (MFS. Maximal Frequent Itemsets are frequent itemsets whichhave no proper frequent superset. Thus, the generation of only maximal frequent itemsets reduces thenumber of itemsets and also time needed for the generation of all frequent itemsets as each maximal itemsetof length m implies the presence of 2m-2 frequent itemsets. Furthermore, mining only maximal frequentitemset is sufficient in many data mining applications like minimal key discovery and theory extraction. Inthis paper, we suggest a novel method for finding the maximal frequent itemset from huge data sourcesusing the concept of segmentation of data source and prioritization of segments. Empirical evaluationshows that this method outperforms various other known methods.
Natural selection and the maximization of fitness.
Birch, Jonathan
2016-08-01
The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. Here I critically appraise the prospects for reconciliation. I first distinguish four varieties of fitness maximization. I then examine two recent developments that may appear to vindicate at least one of these varieties. The first is the 'new' interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions. The second is the Formal Darwinism project, which forges links between gene frequency change and optimal strategy choice. In both cases, I argue that the results fail to establish a biologically significant maximization principle. I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. A more promising approach may be to find maximization principles that apply conditionally and to show that the conditions were satisfied in the evolution of particular traits.
Uncertainty principle in human visual perception
Trifonov, Mikhael I.; Ugolev, Dmitry A.
1994-05-01
The orthodox data concerning the contrast sensitivity estimation for sine-wave gratings were formally analyzed. The result of our analysis made feasible a threshold energy value (Delta) E -- energetic equivalent to quantum of perception -- as (Delta) E equals (alpha) (Delta) L(Delta) X2, where (alpha) is a proportionality coefficient, (Delta) L is a threshold luminance, and (Delta) X is a half-period of grating. The value of (Delta) E is a constant for a given value of mean luminance L of the grating and for a middle spatial frequency region. So the `exchange' between luminance threshold (Delta) L and spatial resolution (Delta) X2 values takes place; the increasing of one is followed by the decreasing of the other. We treated this phenomenon as a principle of uncertainty in human visual perception and proved its correctness for other spatial frequencies. Taking into account threshold wavelength ((Delta) (lambda) ) and time ((Delta) t) the uncertainty principle may be extended to a wider class of visual perception problems, including color and flicker objects recognition. So, we suggest the uncertainty principle proposed above is to be one of the cornerstones of the evolution of cognitive systems.
Quantum speed limits in open system dynamics.
del Campo, A; Egusquiza, I L; Plenio, M B; Huelga, S F
2013-02-01
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics, and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a general, completely positive, and trace preserving evolution which provides a bound to the quantum speed limit. When the evolution is of the Lindblad form, the bound is analogous to the Mandelstam-Tamm relation which applies in the unitary case, with the role of the Hamiltonian being played by the adjoint of the generator of the dynamical semigroup. The utility of the new bound is exemplified in different scenarios, ranging from the estimation of the passage time to the determination of precision limits for quantum metrology in the presence of dephasing noise.
S-parameter uncertainty computations
Vidkjær, Jens
1993-01-01
A method for computing uncertainties of measured s-parameters is presented. Unlike the specification software provided with network analyzers, the new method is capable of calculating the uncertainties of arbitrary s-parameter sets and instrument settings.......A method for computing uncertainties of measured s-parameters is presented. Unlike the specification software provided with network analyzers, the new method is capable of calculating the uncertainties of arbitrary s-parameter sets and instrument settings....
Pauli effects in uncertainty relations
Toranzo, I V; Esquivel, R O; Dehesa, J S
2014-01-01
In this letter we analyze the effect of the spin dimensionality of a physical system in two mathematical formulations of the uncertainty principle: a generalized Heisenberg uncertainty relation valid for all antisymmetric N-fermion wavefunctions, and the Fisher-information- based uncertainty relation valid for all antisymmetric N-fermion wavefunctions of central potentials. The accuracy of these spin-modified uncertainty relations is examined for all atoms from Hydrogen to Lawrencium in a self-consistent framework.
Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
Goyeneche, Dardo; Latorre, José I; Riera, Arnau; Życzkowski, Karol
2015-01-01
Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis novel tensor networks related to holography. We present alternative constructions of AME states and show their link with combinatorial designs. We also analyze a key property of AME, namely their relation to tensors that can be understood as unitary transformations in every of its bi-partitions. We call this property multi-unitarity.
Teleportation of an unknown bipartite state via non-maximally entangled two-particle state
Cao Hai-Jing; Guo Yan-Qing; Song He-Shan
2006-01-01
In this paper a new scheme for teleporting an unknown entangled state of two particles is proposed. To weaken the requirement for the quantum channel, without loss of generality, two communicators only share a non-maximally entangled two-particle state. Teleportation can be probabilistically realized if sender performs Bell-state measurements and Hadamard transformation and receiver introduces two auxiliary particles, operates G-not operation, single-qubit measurements and appropriate unitary transformations. The probability of successful teleportation is determined by the smaller one among the coefficients' absolute values of the quantum channel.
Open timelike curves violate Heisenberg's uncertainty principle.
Pienaar, J L; Ralph, T C; Myers, C R
2013-02-08
Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity.
Uncertainty Relation for Chaos
Yahalom, A; Levitan, J; Elgressy, G; Horwitz, L P; Ben-Zion, Y
2011-01-01
A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples.
Huang, Y C; Zhang, N
2004-01-01
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a general new continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the elec...
Smith, Des H.V.; Converse, Sarah J.; Gibson, Keith; Moehrenschlager, Axel; Link, William A.; Olsen, Glenn H.; Maguire, Kelly
2011-01-01
Captive breeding is key to management of severely endangered species, but maximizing captive production can be challenging because of poor knowledge of species breeding biology and the complexity of evaluating different management options. In the face of uncertainty and complexity, decision-analytic approaches can be used to identify optimal management options for maximizing captive production. Building decision-analytic models requires iterations of model conception, data analysis, model building and evaluation, identification of remaining uncertainty, further research and monitoring to reduce uncertainty, and integration of new data into the model. We initiated such a process to maximize captive production of the whooping crane (Grus americana), the world's most endangered crane, which is managed through captive breeding and reintroduction. We collected 15 years of captive breeding data from 3 institutions and used Bayesian analysis and model selection to identify predictors of whooping crane hatching success. The strongest predictor, and that with clear management relevance, was incubation environment. The incubation period of whooping crane eggs is split across two environments: crane nests and artificial incubators. Although artificial incubators are useful for allowing breeding pairs to produce multiple clutches, our results indicate that crane incubation is most effective at promoting hatching success. Hatching probability increased the longer an egg spent in a crane nest, from 40% hatching probability for eggs receiving 1 day of crane incubation to 95% for those receiving 30 days (time incubated in each environment varied independently of total incubation period). Because birds will lay fewer eggs when they are incubating longer, a tradeoff exists between the number of clutches produced and egg hatching probability. We developed a decision-analytic model that estimated 16 to be the optimal number of days of crane incubation needed to maximize the number of
Pfeiffer, P.; Egusquiza, I. L.; di Ventra, M.; Sanz, M.; Solano, E.
2016-07-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
An introduction to quantum stochastic calculus
Parthasarathy, KR
2012-01-01
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle.Quantum stochastic integration
The equivalence principle in a quantum world
Bjerrum-Bohr, N. Emil J.; Donoghue, John F.; El-Menoufi, Basem Kamal;
2015-01-01
the energy is small, we now have the tools to address this conflict explicitly. Despite the violation of some classical concepts, the EP continues to provide the core of the quantum gravity framework through the symmetry - general coordinate invariance - that is used to organize the effective field theory......We show how modern methods can be applied to quantum gravity at low energy. We test how quantum corrections challenge the classical framework behind the equivalence principle (EP), for instance through introduction of nonlocality from quantum physics, embodied in the uncertainty principle. When...
Teleportations of Mixed States and Multipartite Quantum States
YU Chang-Shui; WANG Ya-Hong; SONG He-Shan
2007-01-01
In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. Ifa non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1 - √1 - C2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation,Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.
ANALYSIS OF INCOMPLETE STOCK MARKET WITH JUMP-DIFFUSION UNCERTAINTY
Xiuli Chao; Indrajit Bardhan
2002-01-01
This paper studies incomplete stock market that includes discontinuous priceprocesses. The discontinuity is modeled by very general point processes admitting onlystochastic intensities. Prices are driven by jump-diffusion uncertainty and have randombut predictable jumps. The space of risk-neutral measures that are associated with themarket is identified and related to fictitious completions. The construction of replicatingportfolios is discussed, and convex duality methods are used to prove existence of optimalconsumption and investment policies for a problem of utility maximization.
Pricing Multi-play Offers under Uncertainty and Competition
Hélène, Le Cadre
2007-01-01
In a mature market, telecommunication operators try to differentiate themselves by marketing bundles offers. In this highly competitive context, operators should anticipate the strategies of their adversaries and guess the consumers' tastes, to maximize their benefits. To price their offers, operators have to deal with deep uncertainties on the other operators' cost structures, strategies, and on the consumers' preferences. We segment the market and estimate the consumers' subjective prices, ...
Quantum Spontaneous Stochasticity
Eyink, Gregory L
2015-01-01
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions for given initial data are unique. In fluid turbulence non-uniqueness due to "roughness" of the advecting velocity field is known to lead to stochastic motion of classical particles. Vanishingly small random perturbations are magnified by Richardson diffusion in a "nearly rough" velocity field so that motion remains stochastic as the noise disappears, or classical spontaneous stochasticity, . Analogies between stochastic particle motion in turbulence and quantum evolution suggest that there should be quantum spontaneous stochasticity (QSS). We show this for 1D models of a particle in a repulsive potential that is "nearly rough" with $V(x) \\sim C|x|^{1+\\alpha}$ at distances $|x|\\gg \\ell$ , for some UV cut-off $\\ell$, and for initial Gaussian wave-packet centered at 0. We consi...
The Second International Workshop on Squeezed States and Uncertainty Relations
Han, D. (Editor); Kim, Y. S.; Manko, V. I.
1993-01-01
This conference publication contains the proceedings of the Second International Workshop on Squeezed States and Uncertainty Relations held in Moscow, Russia, on 25-29 May 1992. The purpose of this workshop was to study possible applications of squeezed states of light. The Workshop brought together many active researchers in squeezed states of light and those who may find the concept of squeezed states useful in their research, particularly in understanding the uncertainty relations. It was found at this workshop that the squeezed state has a much broader implication than the two-photon coherent states in quantum optics, since the squeeze transformation is one of the most fundamental transformations in physics.
Constraining the generalized uncertainty principle with gravitational wave
Feng, Zhong-Wen; Li, Hui-Ling; Zu, Xiao-Tao
2016-01-01
Various theories of quantum gravity suggest a modification in the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP), which produces significant modifications to different physical systems. For this reason, in this paper, we investigate the speed of graviton by utilizing two proposals for the GUP. Then, to comply event GW 150914 data, we set upper bounds on the GUP parameters. It is found that the upper limit of the GUP parameters $\\beta_0$ and $\\alpha_0$ are $1.44675 \\times10^{10}$ and $1.35934 \\times10^{-4}$.
Experimental realization of Popper's Experiment Violation of the Uncertainty Principle?
Kim, Y H; Kim, Yoon-Ho; Shih, Yanhua
1999-01-01
An entangled pair of photons (1 and 2) are emitted to opposite directions. A narrow slit is placed in the path of photon 1 to provide precise knowledge of its position on the $y$ axis and this also determines the precise $y$ position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty in momentum, i.e., a greater $\\Delta p_{y}$, due to the precise knowledge of its position $y$? The experimental data shows historical thought experiment of Karl Popper signal a violation of the uncertainty principle?
Uncertainty quantification in lattice QCD calculations for nuclear physics
Beane, Silas R. [Univ. of Washington, Seattle, WA (United States); Detmold, William [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Orginos, Kostas [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Savage, Martin J. [Institute for Nuclear Theory, Seattle, WA (United States)
2015-02-05
The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. As a result, we review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.
Optimal Energy Management for a Smart Grid using Resource-Aware Utility Maximization
Abegaz, Brook W.; Mahajan, Satish M.; Negeri, Ebisa O.
2016-06-01
Heterogeneous energy prosumers are aggregated to form a smart grid based energy community managed by a central controller which could maximize their collective energy resource utilization. Using the central controller and distributed energy management systems, various mechanisms that harness the power profile of the energy community are developed for optimal, multi-objective energy management. The proposed mechanisms include resource-aware, multi-variable energy utility maximization objectives, namely: (1) maximizing the net green energy utilization, (2) maximizing the prosumers' level of comfortable, high quality power usage, and (3) maximizing the economic dispatch of energy storage units that minimize the net energy cost of the energy community. Moreover, an optimal energy management solution that combines the three objectives has been implemented by developing novel techniques of optimally flexible (un)certainty projection and appliance based pricing decomposition in an IBM ILOG CPLEX studio. A real-world, per-minute data from an energy community consisting of forty prosumers in Amsterdam, Netherlands is used. Results show that each of the proposed mechanisms yields significant increases in the aggregate energy resource utilization and welfare of prosumers as compared to traditional peak-power reduction methods. Furthermore, the multi-objective, resource-aware utility maximization approach leads to an optimal energy equilibrium and provides a sustainable energy management solution as verified by the Lagrangian method. The proposed resource-aware mechanisms could directly benefit emerging energy communities in the world to attain their energy resource utilization targets.
Risk, Uncertainty and Entrepreneurship
Koudstaal, Martin; Sloof, Randolph; Van Praag, Mirjam
Theory predicts that entrepreneurs have distinct attitudes towards risk and uncertainty, but empirical evidence is mixed. To better understand the unique behavioral characteristics of entrepreneurs and the causes of these mixed results, we perform a large ‘lab-in-the-field’ experiment comparing...... entrepreneurs to managers – a suitable comparison group – and employees (n = 2288). The results indicate that entrepreneurs perceive themselves as less risk averse than managers and employees, in line with common wisdom. However, when using experimental incentivized measures, the differences are subtler...
Mathematical Analysis of Uncertainty
Angel GARRIDO
2016-01-01
Full Text Available Classical Logic showed early its insufficiencies for solving AI problems. The introduction of Fuzzy Logic aims at this problem. There have been research in the conventional Rough direction alone or in the Fuzzy direction alone, and more recently, attempts to combine both into Fuzzy Rough Sets or Rough Fuzzy Sets. We analyse some new and powerful tools in the study of Uncertainty, as the Probabilistic Graphical Models, Chain Graphs, Bayesian Networks, and Markov Networks, integrating our knowledge of graphs and probability.
Optimization under Uncertainty
Lopez, Rafael H.
2016-01-06
The goal of this poster is to present the main approaches to optimization of engineering systems in the presence of uncertainties. We begin by giving an insight about robust optimization. Next, we detail how to deal with probabilistic constraints in optimization, the so called the reliability based design. Subsequently, we present the risk optimization approach, which includes the expected costs of failure in the objective function. After that the basic description of each approach is given, the projects developed by CORE are presented. Finally, the main current topic of research of CORE is described.
General conditions for maximal violation of non-contextuality in discrete and continuous variables
Laversanne-Finot, A.; Ketterer, A.; Barros, M. R.; Walborn, S. P.; Coudreau, T.; Keller, A.; Milman, P.
2017-04-01
The contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables. An important property of such observables is that their expectation value can be expressed in terms of probabilities for obtaining two exclusive outcomes. Examples of such inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space. Here we identify the general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics. Our results not only unify existing strategies for maximal violation of state independent non-contextuality inequalities but also lead to new scenarios enabling such violations. Among the consequences of our results is the impossibility of having a state independent maximal violation of non-contextuality in the Peres–Mermin scenario with discrete observables of odd dimensions.
Measurement-based quantum repeaters
Zwerger, M; Briegel, H J
2012-01-01
We introduce measurement-based quantum repeaters, where small-scale measurement-based quantum processors are used to perform entanglement purification and entanglement swapping in a long-range quantum communication protocol. In the scheme, pre-prepared entangled states stored at intermediate repeater stations are coupled with incoming photons by simple Bell-measurements, without the need of performing additional quantum gates or measurements. We show how to construct the required resource states, and how to minimize their size. We analyze the performance of the scheme under noise and imperfections, with focus on small-scale implementations involving entangled states of few qubits. We find measurement-based purification protocols with significantly improved noise thresholds. Furthermore we show that already resource states of small size suffice to significantly increase the maximal communication distance. We also discuss possible advantages of our scheme for different set-ups.
Entanglement properties of quantum polaritons
Suárez-Forero, D. G.; Cipagauta, G.; Vinck-Posada, H.; Fonseca Romero, K. M.; Rodríguez, B. A.; Ballarini, D.
2016-05-01
Exciton polaritons are coupled states of matter and light, originated by the strong interaction between an optical mode and semiconductor excitons. This interaction can be obtained also at a single-particle level, in which case it has been shown that a quantum treatment is mandatory. In this work we study the light-matter entanglement of polaritons from a fully quantum formalism including pumping and dissipation. We find that the entanglement is completely destroyed if the exciton and photon are tuned at the resonance condition, even under very low pumping rates. Instead, the best condition for maximizing entanglement and purity of the steady state is when the exciton and photon are out of resonance and when incoherent pumping exactly compensates the dissipation rate. In the presence of multiple quantum dots coupled to the light mode, matter-light entanglement survives only at larger detuning for a higher number of quantum dots considered.
Chattaraj, Pratim Kumar
2010-01-01
The application of quantum mechanics to many-particle systems has been an active area of research in recent years as researchers have looked for ways to tackle difficult problems in this area. The quantum trajectory method provides an efficient computational technique for solving both stationary and time-evolving states, encompassing a large area of quantum mechanics. Quantum Trajectories brings the expertise of an international panel of experts who focus on the epistemological significance of quantum mechanics through the quantum theory of motion.Emphasizing a classical interpretation of quan
Effects of the Generalized Uncertainty Principle on Compact Stars
Ali, Ahmed Farag
2013-01-01
Based on the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, we investigate the effect of GUP on the thermodynamic properties of compact stars with two different components. We note that the existence of quantum gravity correction tends to resist the collapse of stars if the GUP parameter $\\alpha$ is taking values between Planck scale and electroweak scale. Comparing with approaches, it is found that the radii of compact stars are found smaller. Increasing energy almost exponentially decreases the radii of compact stars.
Optimal conclusive teleportation of quantum states
Roa, L; Fuentes-Guridi, I
2003-01-01
Quantum teleportation of qudits is revisited. In particular, we analyze the case where the quantum channel corresponds to a non-maximally entangled state and show that the success of the protocol is directly related to the problem of distinguishing non-orthogonal quantum states. The teleportation channel can be seen as a coherent superposition of two channels, one of them being a maximally entangled state thus, leading to perfect teleportation and the other, corresponding to a non-maximally entangled state living in a subspace of the d-dimensional Hilbert space. The second channel leads to a teleported state with reduced fidelity. We calculate the average fidelity of the process and show its optimality.
Welfare-maximizing and revenue-maximizing tariffs with a few domestic firms
Bruno Larue; Jean-Philippe Gervais
2002-01-01
In this paper we compare the orthodox optimal tariff formula with the appropriate welfare-maximizing tariff when there are a few producing or importing firms. The welfare-maximizing tariff can be very low, voire negative in some cases, while in others it can even exceed the maximum-revenue tariff. The relationship between the welfare-maximizing tariff and the number of firms need not be monotonically increasing, because the tariff is not strictly used to internalize terms of trade externality...
Maximizing Complementary Quantities by Projective Measurements
M. Souza, Leonardo A.; Bernardes, Nadja K.; Rossi, Romeu
2017-04-01
In this work, we study the so-called quantitative complementarity quantities. We focus in the following physical situation: two qubits ( q A and q B ) are initially in a maximally entangled state. One of them ( q B ) interacts with a N-qubit system ( R). After the interaction, projective measurements are performed on each of the qubits of R, in a basis that is chosen after independent optimization procedures: maximization of the visibility, the concurrence, and the predictability. For a specific maximization procedure, we study in detail how each of the complementary quantities behave, conditioned on the intensity of the coupling between q B and the N qubits. We show that, if the coupling is sufficiently "strong," independent of the maximization procedure, the concurrence tends to decay quickly. Interestingly enough, the behavior of the concurrence in this model is similar to the entanglement dynamics of a two qubit system subjected to a thermal reservoir, despite that we consider finite N. However, the visibility shows a different behavior: its maximization is more efficient for stronger coupling constants. Moreover, we investigate how the distinguishability, or the information stored in different parts of the system, is distributed for different couplings.
Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum
Kourosh Nozari
2013-01-01
Full Text Available We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra [ x , p ] = i ℏ ( 1 − β p + 2 β 2 p 2 , where β is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.
Integrating Out Astrophysical Uncertainties
Fox, Patrick J; Weiner, Neal
2010-01-01
Underground searches for dark matter involve a complicated interplay of particle physics, nuclear physics, atomic physics and astrophysics. We attempt to remove the uncertainties associated with astrophysics by developing the means to map the observed signal in one experiment directly into a predicted rate at another. We argue that it is possible to make experimental comparisons that are completely free of astrophysical uncertainties by focusing on {\\em integral} quantities, such as $g(v_{min})=\\int_{v_{min}} dv\\, f(v)/v $ and $\\int_{v_{thresh}} dv\\, v g(v)$. Direct comparisons are possible when the $v_{min}$ space probed by different experiments overlap. As examples, we consider the possible dark matter signals at CoGeNT, DAMA and CRESST-Oxygen. We find that expected rate from CoGeNT in the XENON10 experiment is higher than observed, unless scintillation light output is low. Moreover, we determine that S2-only analyses are constraining, unless the charge yield $Q_y< 2.4 {\\, \\rm electrons/keV}$. For DAMA t...
Quantum Field Theory on Pseudo-Complex Spacetime
Schuller, F P; Grimm, T W; Schuller, Frederic P.; Wohlfarth, Mattias N.R.; Grimm, Thomas W.
2003-01-01
The pseudo-complex Poincare group encodes both a universal speed and a maximal acceleration, which can be viewed as the kinematics of Born-Infeld electrodynamics. The irreducible representations of this group are constructed, providing the particle spectrum of a relativistic quantum theory that also respects a maximal acceleration. One finds that each standard relativistic particle is associated with a 'pseudo'-partner of equal spin but generically different mass. These pseudo-partners act as Pauli-Villars regulators for the other member of the doublet, as is found from the explicit construction of quantum field theory on pseudo-complex spacetime. Conversely, a Pauli-Villars regularised quantum field theory on real spacetime possesses a field phase space with integrable pseudo-complex structure, which gives rise to a quantum field theory on pseudo-complex spacetime. This equivalence between (i) maximal acceleration kinematics, (ii) pseudo-complex quantum field theory, and (iii) Pauli-Villars regularisation ri...
Quantum Cooperation of Insects
Summhammer, J
2005-01-01
We investigate the cooperation of two insects who share a large number of maximally entangled EPR-pairs to help them decide whether to execute certain actions. In the first example, two ants must push a pebble, which may be too heavy for one ant. In the second example, two distant butterflies must find each other. In both examples the individuals make classical random choices of possible directions, followed by a quantum decision whether to move or to wait. This combination reflects scarce environmental information and the small brain's limited capacity for complex analysis. With quantum mechanical entanglement the two ants can push the pebble up to twice as far as uncorrelated ants, and the two butterflies need only between 48% and 83% of the classical flight path to find each other.
Prediction uncertainty and optimal experimental design for learning dynamical systems
Letham, Benjamin; Letham, Portia A.; Rudin, Cynthia; Browne, Edward P.
2016-06-01
Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.
Decision making uncertainty, imperfection, deliberation and scalability
Kárný, Miroslav; Wolpert, David
2015-01-01
This volume focuses on uncovering the fundamental forces underlying dynamic decision making among multiple interacting, imperfect and selﬁsh decision makers. The chapters are written by leading experts from different disciplines, all considering the many sources of imperfection in decision making, and always with an eye to decreasing the myriad discrepancies between theory and real world human decision making. Topics addressed include uncertainty, deliberation cost and the complexity arising from the inherent large computational scale of decision making in these systems. In particular, analyses and experiments are presented which concern: • task allocation to maximize “the wisdom of the crowd”; • design of a society of “edutainment” robots who account for one anothers’ emotional states; • recognizing and counteracting seemingly non-rational human decision making; • coping with extreme scale when learning causality in networks; • efﬁciently incorporating expert knowledge in personalized...
无
2007-01-01
We present two schemes for preparing remotely a three-particle entangled state by two different quantum channels. In the first scheme, two partial three-particle entangled states are used as the quantum channels, while in the second scheme, three two-particle non-maximally entangled states are employed as the quantum channels. It is shown that the remote state preparation can be successfully realized with certain probability, for both two schemes, if a sender performs some projective measurements and a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.
Polyploidy Induction of Pteroceltis tatarinowii Maxim
Lin ZHANG; Feng WANG; Zhongkui SUN; Cuicui ZHU; Rongwei CHEN
2015-01-01
3%Objective] This study was conducted to obtain tetraploid Pteroceltis tatari-nowi Maxim. with excel ent ornamental traits. [Method] The stem apex growing points of Pteroceltis tatarinowi Maxim. were treated with different concentrations of colchicine solution for different hours to figure out a proper method and obtain poly-ploids. [Result] The most effective induction was obtained by treatment with 0.6%-0.8% colchicine for 72 h with 34.2% mutation rate. Flow cytometry and chromosome observation of the stem apex growing point of P. tatarinowi Maxim. proved that the tetraploid plants were successful y obtained with chromosome number 2n=4x=36. [Conclusion] The result not only fil s the blank of polyploid breeding of P. tatarinowi , but also provides an effective way to broaden the methods of cultivation of fast-growing, high-quality, disease-resilience, new varieties of Pteroceltis.
The maximal process of nonlinear shot noise
Eliazar, Iddo; Klafter, Joseph
2009-05-01
In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay-surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay-surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay-surge structure, and its correlation structure. All results are obtained analytically and in closed-form.
Energy Band Calculations for Maximally Even Superlattices
Krantz, Richard; Byrd, Jason
2007-03-01
Superlattices are multiple-well, semiconductor heterostructures that can be described by one-dimensional potential wells separated by potential barriers. We refer to a distribution of wells and barriers based on the theory of maximally even sets as a maximally even superlattice. The prototypical example of a maximally even set is the distribution of white and black keys on a piano keyboard. Black keys may represent wells and the white keys represent barriers. As the number of wells and barriers increase, efficient and stable methods of calculation are necessary to study these structures. We have implemented a finite-element method using the discrete variable representation (FE-DVR) to calculate E versus k for these superlattices. Use of the FE-DVR method greatly reduces the amount of calculation necessary for the eigenvalue problem.
Quantum robots and quantum computers
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Zurek, Wojciech H [Los Alamos National Laboratory
2008-01-01
Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.
Putz, Volkmar
2015-01-01
We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.
Absence of parasympathetic reactivation after maximal exercise.
de Oliveira, Tiago Peçanha; de Alvarenga Mattos, Raphael; da Silva, Rhenan Bartels Ferreira; Rezende, Rafael Andrade; de Lima, Jorge Roberto Perrout
2013-03-01
The ability of the human organism to recover its autonomic balance soon after physical exercise cessation has an important impact on the individual's health status. Although the dynamics of heart rate recovery after maximal exercise has been studied, little is known about heart rate variability after this type of exercise. The aim of this study is to analyse the dynamics of heart rate and heart rate variability recovery after maximal exercise in healthy young men. Fifteen healthy male subjects (21·7 ± 3·4 years; 24·0 ± 2·1 kg m(-2) ) participated in the study. The experimental protocol consisted of an incremental maximal exercise test on a cycle ergometer, until maximal voluntary exhaustion. After the test, recovery R-R intervals were recorded for 5 min. From the absolute differences between peak heart rate values and the heart rate values at 1 and 5 min of the recovery, the heart rate recovery was calculated. Postexercise heart rate variability was analysed from calculations of the SDNN and RMSSD indexes, in 30-s windows (SDNN(30s) and RMSSD(30s) ) throughout recovery. One and 5 min after maximal exercise cessation, the heart rate recovered 34·7 (±6·6) and 75·5 (±6·1) bpm, respectively. With regard to HRV recovery, while the SDNN(30s) index had a slight increase, RMSSD(30s) index remained totally suppressed throughout the recovery, suggesting an absence of vagal modulation reactivation and, possibly, a discrete sympathetic withdrawal. Therefore, it is possible that the main mechanism associated with the fall of HR after maximal exercise is sympathetic withdrawal or a vagal tone restoration without vagal modulation recovery. © 2012 The Authors Clinical Physiology and Functional Imaging © 2012 Scandinavian Society of Clinical Physiology and Nuclear Medicine.