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Entropy
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Foundations of Quantum Mechanics and Quantum Information Theory
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Foundations of Quantum Mechanics and Quantum Information Theory

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

Deadline for manuscript submissions: closed (31 December 2020) | Viewed by 8013

Special Issue Editors

Dr. Gustavo Martin Bosyk

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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
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
Dr. Federico Holik

E-Mail Website
Guest Editor
Instituto de Física La Plata, CONICET 115 y 49, (1900) La Plata, Argentina
Interests: quantum foundations; quantum information; quantum logic; quantum probability
Special Issues, Collections and Topics in MDPI journals
Dr. Ana Majtey

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Guest Editor
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
Interests: Quantum Information

Special Issue Information

Dear Colleagues,

From the moment of its inception, 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 have given rise to renewed interest in foundational issues. Research in the foundations of quantum mechanics has particularly been influenced by the development of novel laboratory techniques, allowing for the experimental verification of the most debated aspects of the quantum formalism.

The IX Conference on Quantum Foundations (https://sites.google.com/view/ixjfc/home), to be held in November 27–29, 2019, in Córdoba, 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
  • 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
  • Nonlinear methods applied to quantum theory
  • Foundations of relativistic quantum mechanics

Dr. Gustavo Martin Bosyk
Dr. Sebastian Fortin
Dr. Federico Holik
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.

Published Papers (3 papers)

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Research

24 pages, 859 KiB  
Article
Understanding of Various Type of Unambiguous Discrimination in View of Coherence Distribution
by Min Namkung and Younghun Kwon
Entropy 2020, 22(12), 1422; https://0-doi-org.brum.beds.ac.uk/10.3390/e22121422 - 16 Dec 2020
Cited by 3 | Viewed by 1980
Abstract
Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not [...] Read more.
Unambiguous quantum state discrimination is a strategy where the conclusive result can always be trusted. This strategy is very important, since it can be used for various quantum information protocols, including quantum key distribution. However, in the view of quantumness, it is not clear what is going on in performing unambiguous quantum state discrimination. To answer the question, we investigate coherence distribution when unambiguous discrimination is performed by generalized measurement. Specially, we study coherence distribution in three cases, which consist of unambiguous quantum state discrimination, sequential quantum state discrimination, and assisted optimal discrimination, which are considered to be a family of unambiguous quantum state discrimination. In this investigation, we show that the structure of generalized measurements performing various types of unambiguous quantum state discrimination can be understood in terms of coherence distribution. Our result is not limited to the discrimination of two pure quantum states, but it is extended to the discrimination of two mixed states. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics and Quantum Information Theory)
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10 pages, 631 KiB  
Article
The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations
by Richard David Gill
Entropy 2020, 22(3), 287; https://0-doi-org.brum.beds.ac.uk/10.3390/e22030287 - 29 Feb 2020
Cited by 5 | Viewed by 2882
Abstract
The famous singlet correlations of a composite quantum system consisting of two two-level components in the singlet state exhibit notable features of two kinds. One kind are striking certainty relations: perfect anti-correlation, and perfect correlation, under certain joint settings. The other kind [...] Read more.
The famous singlet correlations of a composite quantum system consisting of two two-level components in the singlet state exhibit notable features of two kinds. One kind are striking certainty relations: perfect anti-correlation, and perfect correlation, under certain joint settings. The other kind are a number of symmetries, namely invariance under a common rotation of the settings, invariance under exchange of components, and invariance under exchange of both measurement outcomes. One might like to restrict attention to rotations in the plane since those are the ones most commonly investigated experimentally. One can then also further distinguish between the case of discrete rotations (e.g., only settings which are a whole number of degrees are allowed) and continuous rotations. We study the class of classical correlation functions, i.e., generated by classical physical systems, satisfying all these symmetries, in the continuous, planar, case. We call such correlation functions classical EPR-B correlations. It turns out that if the certainty relations and rotational symmetry holds at the level of the correlations, then rotational symmetry can be imposed “for free” on the underlying classical physical model by adding an extra randomisation level. The other binary symmetries are obtained “for free”. This leads to a simple heuristic description of all possible classical EPR-B correlations in terms of a “spinning bi-coloured disk” model. We deliberately use the word “heuristic” because technical mathematical problems remain wide open concerning the transition from finite or discrete to continuous. The main purpose of this paper is to bring this situation to the attention of the mathematical community. We do show that the widespread idea that “quantum correlations are more extreme than classical physics would allow” is at best highly inaccurate, through giving a concrete example of a classical correlation which satisfies all the symmetries and all the certainty relations and which exceeds the quantum correlations over a whole range of settings. It is found by a search procedure in which we randomly generate classical physical models and, for each generated model, evaluate its properties in a further Monte-Carlo simulation of the model itself. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics and Quantum Information Theory)
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14 pages, 306 KiB  
Article
A First Step to the Categorical Logic of Quantum Programs
by Xin Sun and Feifei He
Entropy 2020, 22(2), 144; https://0-doi-org.brum.beds.ac.uk/10.3390/e22020144 - 24 Jan 2020
Cited by 4 | Viewed by 2553
Abstract
The long-term goal of our research is to develop a powerful quantum logic which is useful in the formal verification of quantum programs and protocols. In this paper we introduce the basic idea of our categorical logic of quantum programs (CLQP): It combines [...] Read more.
The long-term goal of our research is to develop a powerful quantum logic which is useful in the formal verification of quantum programs and protocols. In this paper we introduce the basic idea of our categorical logic of quantum programs (CLQP): It combines the logic of quantum programming (LQP) and categorical quantum mechanics (CQM) such that the advantages of both LQP and CQM are preserved while their disadvantages are overcome. We present the syntax, semantics and proof system of CLQP. As a proof-of-concept, we apply CLQP to verify the correctness of Deutsch’s algorithm and the concealing property of quantum bit commitment. Full article
(This article belongs to the Special Issue Foundations of Quantum Mechanics and Quantum Information Theory)
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