Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.1
Journals
Entropy
Special Issues
Quantum Probability and Randomness V
entropy-logo
Submit to Special Issue Submit Abstract to Special Issue Review for Entropy Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

Quantum Probability and Randomness V

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

Deadline for manuscript submissions: 30 May 2025 | Viewed by 3364

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. Karl Svozil

E-Mail Website
Guest Editor
Institute for Theoretical Physics, Vienna University of Technology Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria
Interests: quantum logic; automaton logic; conventionality in relativity theory; intrinsic embedded observers; physical (in)determinism; physical random number generators; generalized probability theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This is the fifth Special Issue devoted to the theme of “Quantum Probability and Randomness”; for the first four issues, visit the following links:

The previous Special Issues collected a sample of high-quality papers, both theoretical and experiment-related, written by experts in this area, which attracted considerable interest (including numerous downloads). This is why we have decided to proceed once again with this hot topic by considering structuring this theme into a regular series based on the Entropy journal.

The last few years have been characterized by tremendous developments in quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. Despite the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness.

Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meanings of its basic tools, starting with the Born rule, are among the topics which will be covered in this Special Issue.

Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, the quantum probabilistic treatment of problems of the theory of decision making under uncertainty. Such studies are also among the topics addressed in this Special Issue.

The areas covered include the following:

  • Foundations of quantum information theory and quantum probability;
  • Quantum versus classical randomness and quantum random generators;
  • Generalized probabilistic models;
  • Quantum contextuality and generalized contextual models;
  • Bell’s inequality, entanglement, and randomness;
  • Quantum-like probabilistic modeling of the process of decision making under uncertainty;
  • Quantum probabilistic models of cognition and AI;
  • Quantum probability and foundational questions of quantum technologies (computing and cryptography);
  • Quantum probability and information in biology.

Of course, possible topics need not be restricted to the list above; any contribution directed to the improvement of quantum foundations and the development of quantum probability and randomness is welcome.

Prof. Dr. Andrei Khrennikov
Prof. Dr. Karl Svozil
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

  • quantum foundation
  • quantum vs. classical probability and randomness
  • quantum information
  • Bell inequality
  • entanglement
  • contextuality
  • random generators
  • generalized probabilistic models

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Related Special Issues

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

12 pages, 359 KiB  
Article
Statistical Properties of Superpositions of Coherent Phase States with Opposite Arguments
by Miguel Citeli de Freitas and Viktor V. Dodonov
Entropy 2024, 26(11), 977; https://doi.org/10.3390/e26110977 - 15 Nov 2024
Viewed by 320
Abstract
We calculate the second-order moments, the Robertson–Schrödinger uncertainty product, and the Mandel factor for various superpositions of coherent phase states with opposite arguments, comparing the results with similar superpositions of the usual (Klauder–Glauber–Sudarshan) coherent states. We discover that the coordinate variance in the [...] Read more.
We calculate the second-order moments, the Robertson–Schrödinger uncertainty product, and the Mandel factor for various superpositions of coherent phase states with opposite arguments, comparing the results with similar superpositions of the usual (Klauder–Glauber–Sudarshan) coherent states. We discover that the coordinate variance in the analog of even coherent states can show the most strong squeezing effect, close to the maximal possible squeezing for the given mean photon number. On the other hand, the Robertson–Schrödinger (RS) uncertainty product in superpositions of coherent phase states increases much slower (as function of the mean photon number) than in superpositions of the usual coherent states. A nontrivial behavior of the Mandel factor for small mean photon numbers is discovered in superpositions with unequal weights of two components. An exceptional nature of the even and odd superpositions is demonstrated. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
►▼ Show Figures

Figure 1

14 pages, 321 KiB  
Article
On the Negative Result Experiments in Quantum Mechanics
by Kenichi Konishi
Entropy 2024, 26(11), 958; https://doi.org/10.3390/e26110958 - 7 Nov 2024
Viewed by 378
Abstract
We comment on the so-called negative result experiments (also known as null measurements, interaction-free measurements, and so on) in quantum mechanics (QM), in the light of the new general understanding of the quantum-measurement processes, proposed recently. All experiments of this kind (null measurements) [...] Read more.
We comment on the so-called negative result experiments (also known as null measurements, interaction-free measurements, and so on) in quantum mechanics (QM), in the light of the new general understanding of the quantum-measurement processes, proposed recently. All experiments of this kind (null measurements) can be understood as improper measurements with an intentionally biased detector set up, which introduces exclusion or selection of certain events. The prediction on the state of a microscopic system under study based on a null measurement is sometimes dramatically described as “wave-function collapse without any microsystem-detector interactions”. Though certainly correct, such a prediction is just a consequence of the standard QM laws, not different from the situation in the so-called state-preparation procedure. Another closely related concept is the (first-class or) repeatable measurements. The verification of the prediction made by a null measurement requires eventually a standard unbiased measurement involving the microsystem-macroscopic detector interactions, which are nonadiabatic, irreversible processes of signal amplification. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
►▼ Show Figures

Figure 1

28 pages, 347 KiB  
Article
Conditional Values in Quantum Mechanics
by Leon Cohen
Entropy 2024, 26(10), 838; https://doi.org/10.3390/e26100838 - 30 Sep 2024
Viewed by 590
Abstract
We consider the local value of an operator for a given position or momentum and, more generally on the value of another arbitrary observable. We develop a general approach that is based on breaking up Aψ(x) as [...] Read more.
We consider the local value of an operator for a given position or momentum and, more generally on the value of another arbitrary observable. We develop a general approach that is based on breaking up Aψ(x) as Aψ(x)ψ(x)=Aψ(x)ψ(x)R+iAψ(x)ψ(x)I where A is the operator whose local value we seek and ψ(x) is the position wave function. We show that the real part is related to the conditional value for a given position and the imaginary part is related to the standard deviation of the conditional value. We show that the uncertainty of an operator can be expressed in two parts that depend on the real and imaginary parts. In the case of the position representation, the expression for the uncertainty of an operator shows that there are two fundamental contributions, one due to the amplitude of the wave function and the other due to the phase. We obtain the equation of motion for the conditional values, and in particular, we generalize the Ehrenfest theorem by deriving a local version of the theorem. We give a number of examples, including the local value of momentum, kinetic energy, and Hamiltonian. We also discuss other approaches for obtaining a conditional value in quantum mechanics including using quasi-probability distributions and the characteristic function approach, among others. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
23 pages, 388 KiB  
Article
Statistical Signatures of Quantum Contextuality
by Holger F. Hofmann
Entropy 2024, 26(9), 725; https://doi.org/10.3390/e26090725 - 26 Aug 2024
Viewed by 500
Abstract
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to [...] Read more.
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood–Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
►▼ Show Figures

Figure 1

19 pages, 731 KiB  
Article
Correlations in the EPR State Observables
by Daniel F. Orsini, Luna R. N. Oliveira and Marcos G. E. da Luz
Entropy 2024, 26(6), 476; https://doi.org/10.3390/e26060476 - 30 May 2024
Viewed by 858
Abstract
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of [...] Read more.
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of observables describing the composite are equally probable upon measurement, and (b) The absence of concurrence (positive reinforcement) between any of the observables within a particular system; implying that their associated operators do not commute. The so-called EPR states are known to observe (a). Here, we demonstrate in very general (but straightforward) terms that they also satisfy condition (b), a relevant technical fact often overlooked. As an illustration, we work out in detail the three-level systems, i.e., qutrits. Furthermore, given the special characteristics of EPR states (such as maximal entanglement, among others), one might intuitively expect the CHSH correlation, computed exclusively for the observables of qubit EPR states, to yield values greater than two, thereby violating Bell’s inequality. We show such a prediction does not hold true. In fact, the combined properties of (a) and (b) lead to a more limited range of values for the CHSH measure, not surpassing the nonlocality threshold of two. The present constitutes an instructive example of the subtleties of quantum correlations. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop