Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios

Abstract The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpret...

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Autores principales:	Jesús Urías, José Manuel Méndez Martínez
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/f3031e357a76403e87bd1eec57da1a97
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spelling	oai:doaj.org-article:f3031e357a76403e87bd1eec57da1a972021-12-02T11:40:35ZMaximally nonlocal Clauser-Horne-Shimony-Holt scenarios10.1038/s41598-018-24970-32045-2322https://doaj.org/article/f3031e357a76403e87bd1eec57da1a972018-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-24970-3https://doaj.org/toc/2045-2322Abstract The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell’s correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction $$\sqrt{2}-\,1\approx 0.414$$ 2−1≈0.414 of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.Jesús UríasJosé Manuel Méndez MartínezNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-10 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jesús Urías José Manuel Méndez Martínez Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
description	Abstract The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell’s correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction $$\sqrt{2}-\,1\approx 0.414$$ 2−1≈0.414 of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.
format	article
author	Jesús Urías José Manuel Méndez Martínez
author_facet	Jesús Urías José Manuel Méndez Martínez
author_sort	Jesús Urías
title	Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
title_short	Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
title_full	Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
title_fullStr	Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
title_full_unstemmed	Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios
title_sort	maximally nonlocal clauser-horne-shimony-holt scenarios
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/f3031e357a76403e87bd1eec57da1a97
work_keys_str_mv	AT jesusurias maximallynonlocalclauserhorneshimonyholtscenarios AT josemanuelmendezmartinez maximallynonlocalclauserhorneshimonyholtscenarios
_version_	1718395617877688320

Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios

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