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Special Issue "Quantum Information and Communication: From Foundations to Applications"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (20 February 2016)

Special Issue Editors

Guest Editor
Prof. Gregg Jaeger

Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA, USA
E-Mail
Guest Editor
Prof. Dr. Andrei Khrennikov

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, S-35195, Växjö, Sweden
Website | E-Mail
Interests: quantum foundations, information, probability, contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, social and political sciences; p-adic numbers, p-adic and ultrametric analysis, dynamical systems, p-adic theoretical physics, utrametric models of cognition and psychological behavior, p-adic models in geophysics and petroleum research

Special Issue Information

Dear Colleagues,

Recent years have been characterized by a tremendous development of quantum information and communication, both in theory and experiment: quantum computers and, recently, quantum stimulators, cryptography, teleportation, and quantum random generators. It is now clear that this great project is essentially more complex than one would have expected at its initial stage and that its realization demands much more effort on the parts of both theoreticians and experimenters. This is a good time to examine and summarize the results, thus far, of various intensive studies and experimentations regarding, both, successes and difficulties. It is the moment to present expectations of the further developments of the field, to formulate further challenges and problems, and to point out any possible, hidden pitfalls for the future.

The quantum information revolution has significantly increased the interest in the foundations of quantum mechanics. This topic is no longer the business of only philosophers and historians of science, but it is now also largely unavoidable to practicing physicists, theoreticians, and even experimenters. While complemented by the more traditional philosophical analysis, foundational studies are now based, much more firmly, on complex theoretical models, advanced mathematics, and numerical simulations that are very closely related to experiments. The intensive development of quantum information and quantum technologies continually generates novel foundational problems. The problem of distinguishing classical and quantum randomness and justification of the use of quantum random generators, which before was merely a philosophic problem, plays a fundamental role in development of quantum technologies, is one example.

Recently, the mathematical formalism of quantum information theory and quantum probability has provided numerous applications outside of physics, in cognitive and social sciences, psychology, decision-making, economics, psychology, finances, and politics.  In such applications, quantum theory is treated operationally as representing contextual probabilistic behavior of systems of any kind. There are plenty of statistical data, collected in the aforementioned domains of science that do not match the laws of classical probability theory (Kolmogorov, 1933), but can be successfully described and modeled in the framework of quantum theory. Such an approach in the use of quantum formalism is certainly quantum-like, even if a system itself need not necessarily be described by quantum physics; it only exhibits some non-classical information-probabilistic features, and has been exhibited in recent decades, in some situations in quantum optics, which were initially thought to absolutely require quantum entanglement, but were understandable in the absence of it as well, with quantum mechanical formalism being the preferred formal framework in any case.

The aim of this Special Issue is to encourage scientists to present original and recent developments, as well as review papers, on quantum information and communications and the related problems of quantum foundations. Quantum information is treated widely enough to even cover applications of its formalism outside of the physics mentioned above.

One of the objectives of this issue is to promote cross-fertilization among scientists working in a wide range of areas of quantum information, communication and foundations, and theory and applications; for example, interrelation of quantum information theory and theory of open quantum systems, Bell’s inequality, its probabilistic structure and especially its role in theory of quantum random generators, statistical analysis of experimental data, foundations of quantum mechanics, entanglement, and quantum-like models in decision making. One question of especially high interest (in the light of recent experiments in labs of A. Zeilinger and P. Kwiat to close the detection efficiency loophole) is the analysis of the trade-off between entanglement and non-purity of states, leading to violations of the Eberhard and Clauser-Horne versions of Bell’s inequality.

Prof. Gregg Jaeger
Prof. Andrei Khrennikov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum information and communication
  • quantum algorithms and cryptographic protocols
  • quantum and classical probability
  • quantum and classical randomness and random generators
  • entanglement and its measures
  • trade between entanglement and non-purity
  • open quantum systems
  • quantum Markov and non-Markov dynamics
  • theory of quantum apparatuses and instruments
  • contextuality
  • Bell-type inequalities
  • statistical analysis of data
  • quantum-like models of cognition and decision making, in economics, psychology, finances, politics

Published Papers (11 papers)

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Research

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Open AccessArticle Discrete Time Dirac Quantum Walk in 3+1 Dimensions
Entropy 2016, 18(6), 228; doi:10.3390/e18060228
Received: 4 March 2016 / Revised: 28 May 2016 / Accepted: 30 May 2016 / Published: 14 June 2016
Cited by 1 | PDF Full-text (27178 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we consider quantum walks whose evolution converges to the Dirac equation in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two, and three space dimensions. The behaviour of particle states—defined
[...] Read more.
In this paper we consider quantum walks whose evolution converges to the Dirac equation in the limit of small wave-vectors. We show exact Fast Fourier implementation of the Dirac quantum walks in one, two, and three space dimensions. The behaviour of particle states—defined as states smoothly peaked in some wave-vector eigenstate of the walk—is described by an approximated dispersive differential equation that for small wave-vectors gives the usual Dirac particle and antiparticle kinematics. The accuracy of the approximation is provided in terms of a lower bound on the fidelity between the exactly evolved state and the approximated one. The jittering of the position operator expectation value for states having both a particle and an antiparticle component is analytically derived and observed in the numerical implementations. Full article
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Open AccessArticle Quantum Errors and Disturbances: Response to Busch, Lahti and Werner
Entropy 2016, 18(5), 174; doi:10.3390/e18050174
Received: 27 February 2016 / Revised: 25 April 2016 / Accepted: 28 April 2016 / Published: 6 May 2016
Cited by 2 | PDF Full-text (351 KB) | HTML Full-text | XML Full-text
Abstract
Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that
[...] Read more.
Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that omission. We then examine BLW’s criticisms in the light of our analysis. We argue that, although the BLW approach favour (based on the Wasserstein two-deviation) has its uses, there are important physical situations where an operator approach is preferable. We also discuss the reason why the error-disturbance relation is still giving rise to controversies almost a century after Heisenberg first stated his microscope argument. We argue that the source of the difficulties is the problem of interpretation, which is not so wholly disconnected from experimental practicalities as is sometimes supposed. Full article
Open AccessArticle Orthogonal Vector Computations
Entropy 2016, 18(5), 156; doi:10.3390/e18050156
Received: 26 January 2016 / Revised: 1 April 2016 / Accepted: 19 April 2016 / Published: 29 April 2016
Cited by 2 | PDF Full-text (263 KB) | HTML Full-text | XML Full-text
Abstract
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement. Full article
Open AccessArticle Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network
Entropy 2016, 18(4), 151; doi:10.3390/e18040151
Received: 20 February 2016 / Revised: 8 April 2016 / Accepted: 12 April 2016 / Published: 19 April 2016
Cited by 7 | PDF Full-text (2378 KB) | HTML Full-text | XML Full-text
Abstract
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential
[...] Read more.
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM. Full article
Open AccessArticle Interference Energy Spectrum of the Infinite Square Well
Entropy 2016, 18(4), 149; doi:10.3390/e18040149
Received: 26 February 2016 / Revised: 7 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
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Abstract
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros,
[...] Read more.
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction Ψ ( x , t ) with N known zeros located at points s i = ( x i , t i ) . Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle’s quantum state is examined. Full article
Open AccessArticle A Quantum Query Expansion Approach for Session Search
Entropy 2016, 18(4), 146; doi:10.3390/e18040146
Received: 30 January 2016 / Revised: 9 April 2016 / Accepted: 11 April 2016 / Published: 18 April 2016
Cited by 2 | PDF Full-text (1097 KB) | HTML Full-text | XML Full-text
Abstract
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking
[...] Read more.
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking and query expansion. In this paper, we aim to further extend this work by constructing a new superposed state of each document in the information need space, based on which we can incorporate the quantum interference idea in query expansion. We then apply the new quantum query expansion model to session search, which is a typical Web search task. Empirical evaluation on the large-scale Clueweb12 dataset has shown that the proposed model is effective in the session search tasks, demonstrating the potential of developing novel and effective IR models based on intuitions and formalisms of QT. Full article
Open AccessArticle Exploration of Quantum Interference in Document Relevance Judgement Discrepancy
Entropy 2016, 18(4), 144; doi:10.3390/e18040144
Received: 30 January 2016 / Revised: 28 March 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 2 | PDF Full-text (863 KB) | HTML Full-text | XML Full-text
Abstract
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While
[...] Read more.
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While a series of quantum-inspired IR models has been proposed, limited effort has been devoted to verify the existence of the quantum-like phenomenon in real users’ information retrieval processes, from a real user study perspective. In this paper, we aim to explore and model the quantum interference in users’ relevance judgement about documents, caused by the presentation order of documents. A user study in the context of IR tasks have been carried out. The existence of the quantum interference is tested by the violation of the law of total probability and the validity of the order effect. Our main findings are: (1) there is an apparent judging discrepancy across different users and document presentation orders, and empirical data have violated the law of total probability; (2) most search trials recorded in the user study show the existence of the order effect, and the incompatible decision perspectives in the quantum question (QQ) model are valid in some trials. We further explain the judgement discrepancy in more depth, in terms of four effects (comparison, unfamiliarity, attraction and repulsion) and also analyse the dynamics of document relevance judgement in terms of the evolution of the information need subspace. Full article
Open AccessArticle On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics
Entropy 2016, 18(4), 135; doi:10.3390/e18040135
Received: 19 February 2016 / Revised: 30 March 2016 / Accepted: 31 March 2016 / Published: 13 April 2016
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Abstract
De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support
[...] Read more.
De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Peña-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an 1 / r 2 potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium. Full article
Open AccessArticle Disentangling the Quantum World
Entropy 2015, 17(11), 7752-7767; doi:10.3390/e17117752
Received: 22 September 2015 / Revised: 2 November 2015 / Accepted: 6 November 2015 / Published: 16 November 2015
Cited by 7 | PDF Full-text (288 KB) | HTML Full-text | XML Full-text
Abstract
Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a
[...] Read more.
Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a distance, so long as the influence takes a zigzag path, via the intersecting past lightcones of the events in question. Costa de Beauregard’s proposal is related to what has come to be called the retrocausal loophole in Bell’s Theorem, but—like that loophole—it receives little attention, and remains poorly understood. Here we propose a new way to explain and motivate the idea. We exploit some simple symmetries to show how Costa de Beauregard’s zigzag needs to work, to explain the correlations at the core of Bell’s Theorem. As a bonus, the explanation shows how entanglement might be a much simpler matter than the orthodox view assumes—not a puzzling feature of quantum reality itself, but an entirely unpuzzling feature of our knowledge of reality, once zigzags are in play. Full article

Review

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Open AccessReview Entropy? Honest!
Entropy 2016, 18(7), 247; doi:10.3390/e18070247
Received: 11 March 2016 / Revised: 19 May 2016 / Accepted: 3 June 2016 / Published: 30 June 2016
Cited by 3 | PDF Full-text (890 KB) | HTML Full-text | XML Full-text
Abstract
Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description
[...] Read more.
Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons) is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable) generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1) the system’s internal dynamics; (2) unsolicited external influences on it; and (3) the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems! Full article
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Other

Jump to: Research, Review

Open AccessConcept Paper Towards Information Lasers
Entropy 2015, 17(10), 6969-6994; doi:10.3390/e17106969
Received: 11 August 2015 / Revised: 14 September 2015 / Accepted: 29 September 2015 / Published: 16 October 2015
Cited by 4 | PDF Full-text (423 KB) | HTML Full-text | XML Full-text
Abstract
Recently, the methods of quantum theory (QT), especially quantum information and probability, started to be widely applied outside of physics: in cognitive, social and political sciences, psychology, economics, finances, decision making, molecular biology and genetics. Such models can be called quantum-like, in contrast
[...] Read more.
Recently, the methods of quantum theory (QT), especially quantum information and probability, started to be widely applied outside of physics: in cognitive, social and political sciences, psychology, economics, finances, decision making, molecular biology and genetics. Such models can be called quantum-like, in contrast to real quantum physical cognitive and biological models. Quantum-like means that only the information and probability structures of QT are explored. This approach matches the information interpretation of QT well (e.g., Zeilinger and Brukner, Fuchs and Mermin, D’Ariano), as well as the informational viewpoint on physics in general (e.g., Wheeler’s “it from bit” paradigm). In this paper, we propose a quantum-like model of an information laser by precessing the assumptions on the structure of state spaces of information processors, “information atoms” (i-atoms) and information fields. The basic assumption is the discrete structure of state spaces related to quantization of an information analog of energy. To analyze a possible structure of the state space of i-atoms leading to the possibility to create information lasers, we have to develop a purely information version of quantum thermodynamics. We did this by placing the main attention on the derivation of the conditions for the equilibrium of information exchange between i-atoms and a quantized information field. Full article
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Author: Masanao Ozawa
Affiliation: Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan
E-Mail: ozawa@is.nagoya-u.ac.jp

Author: Theo Nieuwenhuizen
Title: On the stability criterion for the hydrogen ground state in Stochastic Electrodynamics
Affiliation: Institute for Theoretical Physics Visitors: Science Park 904, 1098 XH, Amsterdam, the Netherland
E-Mail: T.M.Nieuwenhuizen@uva.nl

Author: Mauro D' Ariano
Affiliation: Dipartimento di Fisica dell’Università degli Studi di Pavia, via Bassi 6, 27100, Pavia, Italy
E-Mail: dariano@unipv.it

Author: Gregg Jaeger
Tentative title: Randomness in measurement-based quantum mechanics
Affiliation: Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA, USA
E-Mail: jaeger@bu.edu

 

Author: Andrei Khrennikov
Tentative title: Towards Information Lasers
Affiliation: International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science Linnaeus University, Växjö-Kalmar, S-35195, Sweden
E-Mail: Andrei.Khrennikov@lnu.se

 

Author: Paul Busch
Tentative title: The failure of root-mean-square value deviation: a quantum effect
Affiliation: Department of Mathematics, University of York, York YO10 5DD, United Kingdom
E-Mail: paul.busch@york.ac.uk

Author: D. Marcus Appleby
Affiliation
: School of Physics, University of Sydney, Sydney, NSW 2006, Australia
E-Mail
: marcus.appleby@gmail.com

Tentative title: Quantum artificial brain
Author: Yoshihisa Yamamoto and Shoko Utsunomiya
Affiliation: Stanford University and National Institute of Informatics
E-Mail: yosihisa@stanford.edu

Tentative title: modelling of information and potential functions
Authors: Haven Emmanuel
Affiliation: School of Management and Institute of Finance, University of Leicester, Leicester, UK
E-Mail: eh76@leicester.ac.uk

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