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Entropy
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Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures
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Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures

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

Deadline for manuscript submissions: closed (15 October 2019) | Viewed by 14615

Special Issue Editors

Dr. Federico Holik

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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 Martin 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 processing; quantum correlations; uncertainty relations; majorization theory and its applications
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Olimpia Lombardi

E-Mail Website
Guest Editor
Institute of Philosophy, CONICET and University of Buenos Aires, Buenos Aires 1406, Argentina
Interests: problem of the arrow of time; interpretation of quantum mechanics; nature of information; foundations of statistical mechanics; philosophy of chemistry
Special Issues, Collections and Topics in MDPI journals
Dr. Sebastian Fortin

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Guest Editor
CONICET, Universidad de Buenos Aires, Departamento de Física, Buenos Aires, Argentina
Interests: interpretation of quantum mechanics; quantum decoherence; classical limit of quantum mechanics; quantum information theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since its origins, quantum theory 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, gave rise to a renewed interest in foundational issues. Research in the foundations of quantum mechanics was particularly influenced by the development of novel laboratory techniques, allowing for the experimental verification of the most debated aspects of the quantum formalism.

The VIII Conference on Quantum Foundations (https://sites.google.com/view/viiijfc), to be held during 21–23 November, 2018, at the CAECE University, Buenos Aires, Argentina, aims to gather experts in the field to promote academic debate on the foundational problems of quantum theory. This Special Issue captures the main aspects of this debate by incorporating a selected list of contributions presented at the conference. Researchers not attending the conference are also 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. Olimpia Lombardi
Dr. Sebastian Fortin
Dr. Federico Holik
Dr. Gustavo M. Bosyk
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 logic
  • quantum correlations
  • uncertainty relations
  • quantum probabilities
  • decoherence and classical limit
  • quantum computing
  • interpretations of quantum mechanics
  • quantum contextuality
  • quantum indistinguishability
  • hidden variable theories

Published Papers (5 papers)

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Research

28 pages, 399 KiB  
Article
Indistinguishability and Negative Probabilities
by J. Acacio de Barros and Federico Holik
Entropy 2020, 22(8), 829; https://doi.org/10.3390/e22080829 - 29 Jul 2020
Cited by 6 | Viewed by 3270
Abstract
In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the [...] Read more.
In this paper, we examined the connection between quantum systems’ indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures)
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16 pages, 307 KiB  
Article
Identical Quantum Particles, Entanglement, and Individuality
by Dennis Dieks
Entropy 2020, 22(2), 134; https://doi.org/10.3390/e22020134 - 23 Jan 2020
Cited by 9 | Viewed by 2673
Abstract
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind (“identical particles”) are completely indistinguishable [...] Read more.
Particles in classical physics are distinguishable objects, which can be picked out individually on the basis of their unique physical properties. By contrast, in the philosophy of physics, the standard view is that particles of the same kind (“identical particles”) are completely indistinguishable from each other and lack identity. This standard view is problematic: Particle indistinguishability is irreconcilable not only with the very meaning of “particle” in ordinary language and in classical physical theory, but also with how this term is actually used in the practice of present-day physics. Moreover, the indistinguishability doctrine prevents a smooth transition from quantum particles to what we normally understand by “particles” in the classical limit of quantum mechanics. Elaborating on earlier work, we here analyze the premises of the standard view and discuss an alternative that avoids these and similar problems. As it turns out, this alternative approach connects to recent discussions in quantum information theory. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures)
17 pages, 1610 KiB  
Article
Entropic Characterization of Quantum States with Maximal Evolution under Given Energy Constraints
by Ana P. Majtey, Andrea Valdés-Hernández, César G. Maglione and Angel R. Plastino
Entropy 2019, 21(8), 770; https://doi.org/10.3390/e21080770 - 07 Aug 2019
Cited by 2 | Viewed by 2837
Abstract
A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, [...] Read more.
A measure D [ t 1 , t 2 ] for the amount of dynamical evolution exhibited by a quantum system during a time interval [ t 1 , t 2 ] is defined in terms of how distinguishable from each other are, on average, the states of the system at different times. We investigate some properties of the measure D showing that, for increasing values of the interval’s duration, the measure quickly reaches an asymptotic value given by the linear entropy of the energy distribution associated with the system’s (pure) quantum state. This leads to the formulation of an entropic variational problem characterizing the quantum states that exhibit the largest amount of dynamical evolution under energy constraints given by the expectation value of the energy. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures)
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17 pages, 386 KiB  
Article
Holistic Type Extension for Classical Logic via Toffoli Quantum Gate
by Hector Freytes, Roberto Giuntini and Giuseppe Sergioli
Entropy 2019, 21(7), 636; https://doi.org/10.3390/e21070636 - 27 Jun 2019
Cited by 2 | Viewed by 2384
Abstract
A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system [...] Read more.
A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of “holistic” contradiction. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures)
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18 pages, 2420 KiB  
Article
Quantum Correlation Based on Uhlmann Fidelity for Gaussian States
by Liang Liu, Jinchuan Hou and Xiaofei Qi
Entropy 2019, 21(1), 6; https://doi.org/10.3390/e21010006 - 22 Dec 2018
Cited by 3 | Viewed by 2729
Abstract
A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the [...] Read more.
A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics: Quantum Logic and Quantum Structures)
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