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Entropy
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Quantum Contextuality and Non-locality: Foundations, Applications and Extensions
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Quantum Contextuality and Non-locality: Foundations, Applications and Extensions

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 1994

Special Issue Editor

Prof. Dr. Samson Abramsky

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Guest Editor
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
Interests: theoretical computer science; quantum information and foundations; game theory

Special Issue Information

Dear Colleagues,

Quantum contextuality is a fundamental non-classical feature of quantum mechanics. Mathematically, non-locality is a special case of contextuality. As well as being central to quantum foundations, these features play a crucial role in most of the known instances of quantum advantage in information processing tasks. Moreover, the mathematical structures characteristic of contextuality also arise in a range of non-quantum settings, from databases to computational linguistics.

We seek submissions which relate to one or more of these aspects of contextuality:

  • The rich mathematical foundations of contextuality, including sheaves and cohomology, graph theory , convex geometry and optimisation, probability, and computational complexity.
  • Current applications of contextuality and non-locality, which include demonstrations of quantum advantage in computational settings such as shallow circuits and communication complexity, randomness amplification, and variational quantum eigensolvers.
  • Connections of contextuality ideas and methods have been found to ideas in logic, databases, constraints, computational linguistics and behavioural science.

We seek papers which develop and extend these ideas, deepen the foundations, and find new areas of application.

Prof. Dr. Samson Abramsky
Guest Editor

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

  • contextuality
  • non-locality
  • contextual inequalities
  • measures of contextuality
  • resource theory of contextuality
  • topology of contextuality
  • cohomological criteria for contextuality
  • graph theoretic parameters
  • quantum advantage
  • contextuality and causality

Published Papers (2 papers)

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Research

11 pages, 265 KiB  
Article
Quantum Mechanics Is Compatible with Counterfactual Definiteness
by Janne V. Kujala and Ehtibar N. Dzhafarov
Entropy 2023, 25(9), 1356; https://doi.org/10.3390/e25091356 - 20 Sep 2023
Viewed by 846
Abstract
Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the [...] Read more.
Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context. It is usually claimed that in quantum mechanics CFD does not hold, because if one assigns the same value to a property in all contexts it is measured in, one runs into a logical contradiction, or at least contravenes quantum theory and experimental evidence. We show that this claim is not substantiated if one takes into account that only one of the possible contexts can be a factual context, all other contexts being counterfactual. With this in mind, any system of random variables can be viewed as satisfying CFD. The concept of CFD is closely related to but distinct from that of noncontextuality, and it is the latter property that may or may not hold for a system, in particular being contravened by some quantum systems. Full article
(This article belongs to the Special Issue Quantum Contextuality and Non-locality: Foundations, Applications and Extensions)
34 pages, 1112 KiB  
Article
Topological Methods for Studying Contextuality: N-Cycle Scenarios and Beyond
by Aziz Kharoof, Selman Ipek and Cihan Okay
Entropy 2023, 25(8), 1127; https://doi.org/10.3390/e25081127 - 27 Jul 2023
Cited by 5 | Viewed by 747
Abstract
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier–Motzkin [...] Read more.
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier–Motzkin elimination and a technique based on the collapsing of measurement spaces. Using the first one, we provide a new proof of Fine’s theorem characterizing noncontextual distributions in N-cycle scenarios. Our approach goes beyond these scenarios and can describe noncontextual distributions in scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions. Full article
(This article belongs to the Special Issue Quantum Contextuality and Non-locality: Foundations, Applications and Extensions)
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