Special Issue "Quantum Information Revolution: Impact to Foundations"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: 15 December 2019.

Special Issue Editors

Prof. Andrei Khrennikov
E-Mail Website
Guest Editor
International Center Math Modeling: Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö, Sweden
Interests: quantum foundations, information, probability, and contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and 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 Issues and Collections in MDPI journals
Prof. Dr. Avshalom C. Elitzur
E-Mail Website
Guest Editor
Bar-Ilan University, Ramat-Gan, Israel
Interests: quantum mechanics, relativity, thermodynamics; evolutionary biology; psychoanalysis and philosophy of mind

Special Issue Information

Dear Colleagues,

The recent quantum information revolution has, not only technological, but also foundational outputs. It completely changes our image of quantum theory, which becomes quantum information theory. In this Special Issue we would like to update the foundational novelty of modern quantum theory. We invite all kinds of contributions devoted not only to coupling of foundations with the quantum information revolution, but also general development of quantum theory and its mathematical formalism, as well as its novel applications, e.g., applications to modeling cognition, biological, social, and political processes.

The areas covered include:

  • Foundations of quantum information theory and quantum probability
  • Generalized probabilistic models
  • Quantum contextuality and generalized contextual models
  • Bell’s inequality, entanglement, quantum nonlocality, hidden variables
  • Weak measurements: theoretical and interpretational questions.
  • Quantum-like models outside physics
  • Derivations of quantum formalism from natural postulates
  • The role the complementarity principle in quantum information theory
  • Complementarity versus contextuality

Of course, possible topics need not be restricted to the list above; any contribution directed to development of quantum foundations and the corresponding mathematical apparatus are welcome.

Prof. Andrei Khrennikov
Prof. Avshalom C. Elitzur
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 1600 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.

Published Papers (7 papers)

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Research

Open AccessArticle
Quantum Games with Unawareness with Duopoly Problems in View
Entropy 2019, 21(11), 1097; https://doi.org/10.3390/e21111097 - 10 Nov 2019
Abstract
Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common [...] Read more.
Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
Open AccessArticle
Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario
Entropy 2019, 21(10), 1012; https://doi.org/10.3390/e21101012 - 18 Oct 2019
Abstract
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control [...] Read more.
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for N = 2 , N = 3 as a function of all involved parameters. We find in the case N = 3 that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
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Open AccessArticle
A Generic Model for Quantum Measurements
Entropy 2019, 21(9), 904; https://doi.org/10.3390/e21090904 - 17 Sep 2019
Cited by 1
Abstract
In previous articles, we presented a derivation of Born’s rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization—physically, the structure of QM results of an interplay between the quantized number of [...] Read more.
In previous articles, we presented a derivation of Born’s rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization—physically, the structure of QM results of an interplay between the quantized number of “modalities” accessible to a quantum system, and the continuum of “contexts” required to define these modalities. In the present article, we provide a unified picture of quantum measurements within our approach, and justify further the role of the system–context dichotomy, and of quantum interferences. We also discuss links with stochastic quantum thermodynamics, and with algebraic quantum theory. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
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Open AccessArticle
Probability Theory as a Physical Theory Points to Superdeterminism
Entropy 2019, 21(9), 848; https://doi.org/10.3390/e21090848 - 30 Aug 2019
Abstract
Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I argue that probability theory points towards superdeterminism, a [...] Read more.
Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I argue that probability theory points towards superdeterminism, a principle that underlies, notably, ‘t Hooft’s Cellular Automaton Interpretation of quantum mechanics. Specifically, I argue that superdeterminism offers a solution for: (1) Kolmogorov’s problem of probabilistic dependence; (2) the interpretation of the Central Limit Theorem; and (3) Bell’s theorem. Superdeterminism’s competitor, indeterminism (“no hidden variables”), remains entirely silent regarding (1) and (2), and leaves (3) as an obstacle rather than a solution for the unification of quantum mechanics and general relativity. This suggests that, if one wishes to stick to the standard position in physics and adopt the principles with the highest explanatory power, one should adopt superdeterminism and reject indeterminism. Throughout the article precise questions to mathematicians are formulated to advance this research. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
Open AccessArticle
Get Rid of Nonlocality from Quantum Physics
Entropy 2019, 21(8), 806; https://doi.org/10.3390/e21080806 - 18 Aug 2019
Abstract
This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of the Bohr complementarity principle. [...] Read more.
This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of the Bohr complementarity principle. Thus, the attempts to couple experimental violations of the Bell type inequalities with “quantum nonlocality” is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single electron or the polarization projections for a single photon. Of course, one can go beyond quantum theory with the hidden variables models (as was suggested by Bell) and then discuss their possible nonlocal features. However, conventional quantum theory is local. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
Open AccessArticle
PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation
Entropy 2019, 21(2), 105; https://doi.org/10.3390/e21020105 - 23 Jan 2019
Cited by 2
Abstract
The Accardi–Boukas quantum Black–Scholes framework, provides a means by which one can apply the Hudson–Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers–Moyal expansion, and this provides useful tools to [...] Read more.
The Accardi–Boukas quantum Black–Scholes framework, provides a means by which one can apply the Hudson–Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers–Moyal expansion, and this provides useful tools to understand their behaviour. In this paper we develop further links between quantum stochastic processes, and nonlocal diffusions, by inverting the question, and showing how certain nonlocal diffusions can be written as quantum stochastic processes. We then go on to show how one can use path integral formalism, and PT symmetric quantum mechanics, to build a non-Gaussian kernel function for the Accardi–Boukas quantum Black–Scholes. Behaviours observed in the real market are a natural model output, rather than something that must be deliberately included. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)
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Open AccessArticle
Logical Structures Underlying Quantum Computing
Entropy 2019, 21(1), 77; https://doi.org/10.3390/e21010077 - 16 Jan 2019
Cited by 1
Abstract
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures. Full article
(This article belongs to the Special Issue Quantum Information Revolution: Impact to Foundations)

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.

Tentative title: Application of theory of quantum instruments to psychology: Combination of question order effect with response replicability effect
Authors: Masanao Ozawa and Andrei Khrennikov

Tentative title: A note on complexities by means of quatum compound systems
Author: Noboru Watanabe

Tentative title: On Exchange Forces in Quantum Mechanics
Author: Gregg Jaeger

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