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Entropy
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Towards Ultimate Quantum Theory (UQT)
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Towards Ultimate Quantum Theory (UQT)

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

Deadline for manuscript submissions: closed (10 October 2018) | Viewed by 45072

Special Issue Editors

Prof. Dr. Andrei Khrennikov

E-Mail Website
Guest Editor
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; 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, Collections and Topics in MDPI journals
Prof. Dr. Margarita A. Man’ko

E-Mail Website
Guest Editor
Lebedev Physical Institute, Leninskii Prospect 53, 119991 Moscow, Russia
Interests: interpretations of quantum mechanics; the probabilistic structure of Bell’s inequality; quantum and classical probability; entanglement and Bell-type inequalities; quantum optics
Special Issues, Collections and Topics in MDPI journals
Dr. Yutaka Shikano

E-Mail Website
Guest Editor
Quantum Computing Center, Keio University, Yokohama 223-8522, Japan
Interests: quantum measurement theory; quantum information science; quantum random walk

Special Issue Information

Dear Colleagues,

In spite of its tremendous success (both theoretical and experimental), the present quantum theory cannot be considered as the ultimate theory of micro-phenomena. It suffers from a variety of fundamental problems. Quantum mechanics is a nonrelativistic theory and its relativistic generalization, quantum field theory, suffers of divergences. However, of course, the biggest black cloud in the quantum sky is the impossibility to unify presently-existing quantum theory with general relativity. This Special Issue will be devoted to searching for new ways to create an ultimate quantum theory. However, since this project can take very long time (and even it may happen that it is never finished), the issue also covers all traditional foundational topics: Interpretations, measurement theory, quantum information, entanglement and Bell-type inequalities, mathematical apparatus, experiment and its statistical analysis, quantum versus classical probability and randomness, quantum versus classical random walk, applications of the quantum formalism outside of physics, and especially applications of the principle of complementarity in cognition and decision making.

Prof. Andrei Khrennikov
Dr. Margarita A. Man’ko
Dr. Yutaka Shikano
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 submissions that pass pre-check are 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 2600 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

  • Interpretations of quantum mechanics
  • Quantum mechanics as emergent theory
  • Ontic and epistemic models
  • Bild concept in quantum mechanics
  • Quantum information and communication
  • Quantum and classical probability
  • Quantum and classical randomness and random generators
  • Entanglement and Bell-type inequalities
  • Theory of quantum apparatuses and instruments
  • Contextuality
  • Statistical analysis of data
  • Quantum-like models of cognition and decision making, in economics, psychology, finances, politics

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (7 papers)

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Research

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17 pages, 269 KiB  
Article
Are Virtual Particles Less Real?
by Gregg Jaeger
Entropy 2019, 21(2), 141; https://doi.org/10.3390/e21020141 - 2 Feb 2019
Cited by 22 | Viewed by 11596
Abstract
The question of whether virtual quantum particles exist is considered here in light of previous critical analysis and under the assumption that there are particles in the world as described by quantum field theory. The relationship of the classification of particles to quantum-field-theoretic [...] Read more.
The question of whether virtual quantum particles exist is considered here in light of previous critical analysis and under the assumption that there are particles in the world as described by quantum field theory. The relationship of the classification of particles to quantum-field-theoretic calculations and the diagrammatic aids that are often used in them is clarified. It is pointed out that the distinction between virtual particles and others and, therefore, judgments regarding their reality have been made on basis of these methods rather than on their physical characteristics. As such, it has obscured the question of their existence. It is here argued that the most influential arguments against the existence of virtual particles but not other particles fail because they either are arguments against the existence of particles in general rather than virtual particles per se, or are dependent on the imposition of classical intuitions on quantum systems, or are simply beside the point. Several reasons are then provided for considering virtual particles real, such as their descriptive, explanatory, and predictive value, and a clearer characterization of virtuality—one in terms of intermediate states—that also applies beyond perturbation theory is provided. It is also pointed out that in the role of force mediators, they serve to preclude action-at-a-distance between interacting particles. For these reasons, it is concluded that virtual particles are as real as other quantum particles. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
17 pages, 351 KiB  
Article
Closing the Door on Quantum Nonlocality
by Marian Kupczynski
Entropy 2018, 20(11), 877; https://doi.org/10.3390/e20110877 - 15 Nov 2018
Cited by 21 | Viewed by 4565
Abstract
Bell-type inequalities are proven using oversimplified probabilistic models and/or counterfactual definiteness (CFD). If setting-dependent variables describing measuring instruments are correctly introduced, none of these inequalities may be proven. In spite of this, a belief in a mysterious quantum nonlocality is not fading. Computer [...] Read more.
Bell-type inequalities are proven using oversimplified probabilistic models and/or counterfactual definiteness (CFD). If setting-dependent variables describing measuring instruments are correctly introduced, none of these inequalities may be proven. In spite of this, a belief in a mysterious quantum nonlocality is not fading. Computer simulations of Bell tests allow people to study the different ways in which the experimental data might have been created. They also allow for the generation of various counterfactual experiments’ outcomes, such as repeated or simultaneous measurements performed in different settings on the same “photon-pair”, and so forth. They allow for the reinforcing or relaxing of CFD compliance and/or for studying the impact of various “photon identification procedures”, mimicking those used in real experiments. Data samples consistent with quantum predictions may be generated by using a specific setting-dependent identification procedure. It reflects the active role of instruments during the measurement process. Each of the setting-dependent data samples are consistent with specific setting-dependent probabilistic models which may not be deduced using non-contextual local realistic or stochastic hidden variables. In this paper, we will be discussing the results of these simulations. Since the data samples are generated in a locally causal way, these simulations provide additional strong arguments for closing the door on quantum nonlocality. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
22 pages, 1533 KiB  
Article
Logical Entropy: Introduction to Classical and Quantum Logical Information Theory
by David Ellerman
Entropy 2018, 20(9), 679; https://doi.org/10.3390/e20090679 - 6 Sep 2018
Cited by 16 | Viewed by 6481
Abstract
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using [...] Read more.
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions (“dits”) of a partition (a pair of points distinguished by the partition). All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates (cohered together in the pure superposition state being measured) that are distinguished by the measurement (decohered in the post-measurement mixed state). Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
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17 pages, 5626 KiB  
Article
Geometry and Entanglement of Two-Qubit States in the Quantum Probabilistic Representation
by Julio Alberto López-Saldívar, Octavio Castaños, Eduardo Nahmad-Achar, Ramón López-Peña, Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2018, 20(9), 630; https://doi.org/10.3390/e20090630 - 24 Aug 2018
Cited by 28 | Viewed by 4850
Abstract
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres–Horodecki positive partial transpose (ppt) -criterion and the concurrence inequalities are formulated as the [...] Read more.
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres–Horodecki positive partial transpose (ppt) -criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevich’s squares for entangled states of two qubits are defined through the qutrit state, and the critical values of the sum of their areas are calculated. We always find an interval for the sum of the square areas, which provides the possibility for an experimental checkup of the entanglement of the system in terms of the probabilities. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
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17 pages, 411 KiB  
Article
Quantum Games with Unawareness
by Piotr Frąckiewicz
Entropy 2018, 20(8), 555; https://doi.org/10.3390/e20080555 - 26 Jul 2018
Cited by 5 | Viewed by 3997
Abstract
Games with unawareness model strategic situations in which players’ perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as well as the players [...] Read more.
Games with unawareness model strategic situations in which players’ perceptions about the game are limited. They take into account the fact that the players may be unaware of some of the strategies available to them or their opponents as well as the players may have a restricted view about the number of players participating in the game. The aim of the paper is to introduce this notion into theory of quantum games. We focus on games in strategic form and Eisert–Wilkens–Lewenstein type quantum games. It is shown that limiting a player’s perception in the game enriches the structure of the quantum game substantially and allows the players to obtain results that are unattainable when the game is played in a quantum way by means of previously used methods. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
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Review

Jump to: Research

20 pages, 333 KiB  
Review
Classical (Local and Contextual) Probability Model for Bohm–Bell Type Experiments: No-Signaling as Independence of Random Variables
by Andrei Khrennikov and Alexander Alodjants
Entropy 2019, 21(2), 157; https://doi.org/10.3390/e21020157 - 8 Feb 2019
Cited by 40 | Viewed by 4852
Abstract
We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper [...] Read more.
We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm–Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm–Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
13 pages, 1205 KiB  
Review
The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments
by Yakir Aharonov, Eliahu Cohen, Mordecai Waegell and Avshalom C. Elitzur
Entropy 2018, 20(11), 854; https://doi.org/10.3390/e20110854 - 7 Nov 2018
Cited by 18 | Viewed by 7090
Abstract
While quantum reality can be probed through measurements, the Two-State Vector Formalism (TSVF) reveals a subtler reality prevailing between measurements. Under special pre- and post-selections, odd physical values emerge. This unusual picture calls for a deeper study. Instead of the common, wave-based picture [...] Read more.
While quantum reality can be probed through measurements, the Two-State Vector Formalism (TSVF) reveals a subtler reality prevailing between measurements. Under special pre- and post-selections, odd physical values emerge. This unusual picture calls for a deeper study. Instead of the common, wave-based picture of quantum mechanics, we suggest a new, particle-based perspective: Each particle possesses a definite location throughout its evolution, while some of its physical variables (characterized by deterministic operators, some of which obey nonlocal equations of motion) are carried by “mirage particles” accounting for its unique behavior. Within the time interval between pre- and post-selection, the particle gives rise to a horde of such mirage particles, of which some can be negative. What appears to be “no-particle”, known to give rise to interaction-free measurement, is in fact a self-canceling pair of positive and negative mirage particles, which can be momentarily split and cancel out again. Feasible experiments can give empirical evidence for these fleeting phenomena. In this respect, the Heisenberg ontology is shown to be conceptually advantageous compared to the Schrödinger picture. We review several recent advances, discuss their foundational significance and point out possible directions for future research. Full article
(This article belongs to the Special Issue Towards Ultimate Quantum Theory (UQT))
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