Graph-theoretic approach for self-testing in Bell scenarios

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ...

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Autores: Bharti, Kishor, Ray, Maharshi, Xu, Zhen Peng, Hayashi, Masahito, Kwek, Leong Chuan, Cabello Quintero, Adán
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/144667
Acesso em linha:https://hdl.handle.net/11441/144667
https://doi.org/10.1103/PRXQuantum.3.030344
Access Level:acceso abierto
Palavra-chave:Graph-Theoretic approach
Self-testing
Bell scenarios
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spelling Graph-theoretic approach for self-testing in Bell scenariosBharti, KishorRay, MaharshiXu, Zhen PengHayashi, MasahitoKwek, Leong ChuanCabello Quintero, AdánGraph-Theoretic approachSelf-testingBell scenariosSelf-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that BQ is strictly contained in an easy-to-characterize set associated with a graph, (G). Therefore, whenever the optimum over BQ and the optimum over (G) coincide, self-testing can be demonstrated by simply proving self-testability with (G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.American Physical SocietyFísica Aplicada IIFQM239: Fundamentos de Mecánica Cuántica2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/144667https://doi.org/10.1103/PRXQuantum.3.030344reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésPRX Quantum, 3 (030344).https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.030344info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1446672026-06-17T12:51:07Z
dc.title.none.fl_str_mv Graph-theoretic approach for self-testing in Bell scenarios
title Graph-theoretic approach for self-testing in Bell scenarios
spellingShingle Graph-theoretic approach for self-testing in Bell scenarios
Bharti, Kishor
Graph-Theoretic approach
Self-testing
Bell scenarios
title_short Graph-theoretic approach for self-testing in Bell scenarios
title_full Graph-theoretic approach for self-testing in Bell scenarios
title_fullStr Graph-theoretic approach for self-testing in Bell scenarios
title_full_unstemmed Graph-theoretic approach for self-testing in Bell scenarios
title_sort Graph-theoretic approach for self-testing in Bell scenarios
dc.creator.none.fl_str_mv Bharti, Kishor
Ray, Maharshi
Xu, Zhen Peng
Hayashi, Masahito
Kwek, Leong Chuan
Cabello Quintero, Adán
author Bharti, Kishor
author_facet Bharti, Kishor
Ray, Maharshi
Xu, Zhen Peng
Hayashi, Masahito
Kwek, Leong Chuan
Cabello Quintero, Adán
author_role author
author2 Ray, Maharshi
Xu, Zhen Peng
Hayashi, Masahito
Kwek, Leong Chuan
Cabello Quintero, Adán
author2_role author
author
author
author
author
dc.contributor.none.fl_str_mv Física Aplicada II
FQM239: Fundamentos de Mecánica Cuántica
dc.subject.none.fl_str_mv Graph-Theoretic approach
Self-testing
Bell scenarios
topic Graph-Theoretic approach
Self-testing
Bell scenarios
description Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that BQ is strictly contained in an easy-to-characterize set associated with a graph, (G). Therefore, whenever the optimum over BQ and the optimum over (G) coincide, self-testing can be demonstrated by simply proving self-testability with (G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/144667
https://doi.org/10.1103/PRXQuantum.3.030344
url https://hdl.handle.net/11441/144667
https://doi.org/10.1103/PRXQuantum.3.030344
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv PRX Quantum, 3 (030344).
https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.030344
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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