Rényi Entropy, Signed Probabilities, and the Qubit

The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point pha...

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Autores principales: Brandenburger, Adam, La Mura, Pierfrancesco, Zoble, Stuart
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9602278/
https://www.ncbi.nlm.nih.gov/pubmed/37420432
http://dx.doi.org/10.3390/e24101412
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author Brandenburger, Adam
La Mura, Pierfrancesco
Zoble, Stuart
author_facet Brandenburger, Adam
La Mura, Pierfrancesco
Zoble, Stuart
author_sort Brandenburger, Adam
collection PubMed
description The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states.
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spelling pubmed-96022782022-10-27 Rényi Entropy, Signed Probabilities, and the Qubit Brandenburger, Adam La Mura, Pierfrancesco Zoble, Stuart Entropy (Basel) Article The states of the qubit, the basic unit of quantum information, are 2 × 2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states. MDPI 2022-10-03 /pmc/articles/PMC9602278/ /pubmed/37420432 http://dx.doi.org/10.3390/e24101412 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Brandenburger, Adam
La Mura, Pierfrancesco
Zoble, Stuart
Rényi Entropy, Signed Probabilities, and the Qubit
title Rényi Entropy, Signed Probabilities, and the Qubit
title_full Rényi Entropy, Signed Probabilities, and the Qubit
title_fullStr Rényi Entropy, Signed Probabilities, and the Qubit
title_full_unstemmed Rényi Entropy, Signed Probabilities, and the Qubit
title_short Rényi Entropy, Signed Probabilities, and the Qubit
title_sort rényi entropy, signed probabilities, and the qubit
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9602278/
https://www.ncbi.nlm.nih.gov/pubmed/37420432
http://dx.doi.org/10.3390/e24101412
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AT zoblestuart renyientropysignedprobabilitiesandthequbit

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