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Entropy
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Axiomatic Approaches to Quantum Mechanics
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Axiomatic Approaches to Quantum Mechanics

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

Deadline for manuscript submissions: closed (15 September 2021)

Special Issue Editors

Dr. Avishy Carmi

E-Mail Website
Guest Editor
Faculty of Engineering Sciences and Center for Quantum Information Science and Tech-nology, Ben-Gurion University of the Negev, Beersheba, Israel
Interests: classical and quantum information processing; quantum nonlocality; estimation theory; filtering theory; information processing; complex and multi-agent systems; natural; quantum and unconventional computation
Special Issues, Collections and Topics in MDPI journals
Dr. Eliahu Cohen

E-Mail Website
Guest Editor
Faculty of Engineering, Institute for Nanotechnology&Advanced Materials, and Center for Quantum Entanglement Science&Technology, Bar-Ilan University, Ramat-Gan 5290002, Israel
Interests: quantum mechanics; quantum information; quantum optics; quantum field theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

The basic principles of quantum mechanics, which work so well in the lab, have always given rise to intensive conceptual debates. Alongside the search for better understanding of those principles, researchers have tried over the years to ground the mathematical structure of quantum mechanics with a small set of physically plausible assumptions. In recent decades, attempts have been made, for example, at deriving the set of quantum nonlocal correlations and the Born rule from information-theoretic and other sensible axioms. More recently, axiomatic approaches subsumed quantum field theory and the foundations of quantum thermodynamics. In addition, many glimpses have been made beyond the quantum formalism, e.g., attempts to relax some of the axioms of quantum mechanics in order to generalize it, possibly towards a quantum theory of gravity.

We now invite submissions related to the following topics:

  • Derivation from first principles of:
    • Nonlocal quantum correlations or quantum entanglement;
    • Quantum contextuality;
    • Born rule;
    • Schrödinger/Heisenberg/Dirac/Klein-Gordon/GKLS/ equations;
    • Geometric or algebraic structure of quantum mechanics;
  • Quantization methods;
  • Collapse mechanisms;
  • Quantum uncertainty;
  • Fundamental comparison between quantum and classical effects;
  • Fundamental comparison between quantum and post-quantum effects;
  • Fundamentals of quantum thermodynamics;
  • Axiomatic quantum field theory;
  • Fundamental basis for quantum gravity theories;
  • Generalizations of quantum mechanics.

Dr. Avishy Carmi
Dr. Eliahu Cohen
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 mechanics
  • Quantum information
  • Quantum field theory
  • Quantum thermodynamics
  • Quantum gravity

Published Papers (3 papers)

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Research

19 pages, 533 KiB  
Article
Uncertainty Relation between Detection Probability and Energy Fluctuations
by Felix Thiel, Itay Mualem, David Kessler and Eli Barkai
Entropy 2021, 23(5), 595; https://0-doi-org.brum.beds.ac.uk/10.3390/e23050595 - 11 May 2021
Cited by 5 | Viewed by 1874
Abstract
A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic [...] Read more.
A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations. Full article
(This article belongs to the Special Issue Axiomatic Approaches to Quantum Mechanics)
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25 pages, 350 KiB  
Article
The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
by Massimo Tessarotto and Claudio Cremaschini
Entropy 2020, 22(11), 1209; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111209 - 26 Oct 2020
Cited by 6 | Viewed by 2133
Abstract
The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of [...] Read more.
The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated. Full article
(This article belongs to the Special Issue Axiomatic Approaches to Quantum Mechanics)
9 pages, 251 KiB  
Article
Quantum Contextuality and Indeterminacy
by Gregg Jaeger
Entropy 2020, 22(8), 867; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080867 - 07 Aug 2020
Cited by 10 | Viewed by 2564
Abstract
The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of [...] Read more.
The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior. Full article
(This article belongs to the Special Issue Axiomatic Approaches to Quantum Mechanics)
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