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Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum...
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Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 9483

Special Issue Editors

Dr. Federico Holik

E-Mail Website
Guest Editor
Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata 1900, Argentina
Interests: foundations of quantum mechanics; quantum information theory; quantum probabilities; quantum logic
Special Issues, Collections and Topics in MDPI journals
Dr. Gustavo Martín Bosyk

E-Mail Website
Guest Editor
1. Instituto de Física La Plata (IFLP), CONICET, UNLP, Diagonal 113 e/63 y 64, 1900 La Plata, Argentina;
2. Università degli Studi di Cagliari, I-09123 Cagliari, Italy
Interests: quantum information; quantum correlations; uncertainty relations; majorization theory and its applications; entropies
Special Issues, Collections and Topics in MDPI journals
Dr. Ana Majtey

E-Mail Website
Guest Editor
Instituto de Física Enrique Gaviola, CONICET, Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
Interests: quantum mechanics; quantum information; quantum dynamics; ultracold atoms

Special Issue Information

Dear Colleagues,

Since its origins, quantum theory has posed deep questions with regard to the fundamental problems of physics. During the last few decades, the advent of quantum information theory and the possibility of developing quantum computers has given rise to renewed interest in foundational issues. Research into the foundations of quantum mechanics has been particularly influenced by the development of novel laboratory techniques, allowing for experimental verification of the most debated aspects of quantum formalism.

The X Conference on Quantum Foundations, to be held online during November 2021, aims to gather experts in the field with the purpose of promoting academic debate on the foundational problems of quantum theory. For ten years, this conference has served as a forum for heated debate, bringing together researchers from various parts of the world. This Special Issue aims to contribute to the development of that debate. Researchers interested in quantum foundations are welcome to present their original and recent developments, as well as review papers, on the topics listed below. All contributions will be peer-reviewed.

Topics of the Special Issue:

  • Quantum Information Science
  • Quantum Statistical Mechanics
  • Information Measures in Quantum Theory
  • Quantum Correlations
  • Uncertainty relations
  • Geometrical Methods Applied to Quantum Theory
  • Violation of Bell Inequalities
  • Quantum Probabilities
  • Decoherence and Classical Limit
  • Quantum Computing
  • Interpretations of Quantum Mechanics
  • Quantum Contextuality
  • Quantum Indistinguishability
  • Quantum Logic
  • Algebraic Methods in Quantum Theory
  • Hidden Variable Theories
  • Non-linear Methods Applied to Quantum Theory
  • Foundations of Relativistic Quantum Mechanics

Dr. Federico Holik
Dr. Gustavo Martín Bosyk
Dr. Ana Majtey
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 correlations
  • decoherence and classical limit
  • uncertainty relations
  • quantum probabilities
  • quantum computing
  • interpretations of quantum mechanics
  • quantum contextuality
  • quantum indistinguishability
  • quantum logic
  • hidden variable theories

Published Papers (5 papers)

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Research

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14 pages, 310 KiB  
Article
Intrinsic Information-Theoretic Models
by D. Bernal-Casas and J. M. Oller
Entropy 2024, 26(5), 370; https://doi.org/10.3390/e26050370 - 28 Apr 2024
Viewed by 406
Abstract
With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate [...] Read more.
With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (μ, σ0), as before, but with a constant σ0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution Nm(μ,Σ0) with a constant variance–covariance matrix Σ0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ0, altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
10 pages, 283 KiB  
Article
Information-Theoretic Models for Physical Observables
by D. Bernal-Casas and J. M. Oller
Entropy 2023, 25(10), 1448; https://doi.org/10.3390/e25101448 - 14 Oct 2023
Cited by 1 | Viewed by 1104
Abstract
This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space [...] Read more.
This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger’s equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator’s variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator’s variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér–Rao lower bound on the estimator’s variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger’s recent statement that the world is not broken into physical but informational parts. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
32 pages, 460 KiB  
Article
Mathematical Models for Unstable Quantum Systems and Gamow States
by Manuel Gadella, Sebastián Fortín, Juan Pablo Jorge and Marcelo Losada
Entropy 2022, 24(6), 804; https://doi.org/10.3390/e24060804 - 08 Jun 2022
Cited by 3 | Viewed by 2083
Abstract
We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some [...] Read more.
We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
17 pages, 578 KiB  
Article
An Holistic Extension for Classical Logic via Quantum Fredkin Gate
by Hector Freytes and Giuseppe Sergioli
Entropy 2021, 23(9), 1178; https://doi.org/10.3390/e23091178 - 07 Sep 2021
Viewed by 1465
Abstract
An holistic extension for classical propositional logic is introduced in the framework of quantum computation with mixed states. The mentioned extension is obtained by applying the quantum Fredkin gate to non-factorizable bipartite states. In particular, an extended notion of classical contradiction is studied [...] Read more.
An holistic extension for classical propositional logic is introduced in the framework of quantum computation with mixed states. The mentioned extension is obtained by applying the quantum Fredkin gate to non-factorizable bipartite states. In particular, an extended notion of classical contradiction is studied in this holistic framework. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
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Review

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16 pages, 321 KiB  
Review
Collapse Models: A Theoretical, Experimental and Philosophical Review
by Angelo Bassi, Mauro Dorato and Hendrik Ulbricht
Entropy 2023, 25(4), 645; https://doi.org/10.3390/e25040645 - 12 Apr 2023
Cited by 7 | Viewed by 2891
Abstract
In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In [...] Read more.
In this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to the three parts of the paper. In any empirical science, the first two features are obviously connected but, as is well known, among the different formulations and interpretations of non-relativistic quantum mechanics, only collapse models, as the paper well illustrates with a richness of details, have experimental consequences. Finally, we show that a clarification of the ontological intimations of collapse models is needed for at least three reasons: (1) to respond to the indispensable task of answering the question ’what are collapse models (and in general any physical theory) about?’; (2) to achieve a deeper understanding of their different formulations; (3) to enlarge the panorama of possible readings of a theory, which historically has often played a fundamental heuristic role. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Reversibility and Time Arrow in Quantum Theory)
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