Quantum state-independent contextuality requires 13 rays

We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three (2012 Phys. Rev. Lett. 108 030402) is actually the minimal set in quantum t...

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Autores: Cabello Quintero, Adán, Kleinmann, Matthias, Portillo Fernández, José Ramón
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2016
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/135955
Acceso en línea:https://hdl.handle.net/11441/135955
https://doi.org/10.1088/1751-8113/49/38/38LT01
Access Level:acceso abierto
Palabra clave:Quantum contextuality
Kochen–Specker theorem
Graph theory
foundations of quantum physics
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spelling Quantum state-independent contextuality requires 13 raysCabello Quintero, AdánKleinmann, MatthiasPortillo Fernández, José RamónQuantum contextualityKochen–Specker theoremGraph theoryfoundations of quantum physicsWe show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three (2012 Phys. Rev. Lett. 108 030402) is actually the minimal set in quantum theory. This contrasts with the case of Kochen–Specker sets, where the smallest set occurs in dimension four.Ministerio de Economía y Competitividad FIS2014-60843-PIOP ScienceMatemática Aplicada IFísica Aplicada IIFQM-164: Matemática Discreta: Teoría de Grafos y Geometría ComputacionalFQM-239: Fundamentos de Mecánica CuánticaMinisterio de Economía y Competitividad (MINECO). España2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/135955https://doi.org/10.1088/1751-8113/49/38/38LT01reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Physics A: Mathematical and Theoretical, 49 (38), 38LT01-1-38LT01-9.FIS2014-60843-Phttps://iopscience.iop.org/article/10.1088/1751-8113/49/38/38LT01info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1359552026-06-17T12:51:07Z
dc.title.none.fl_str_mv Quantum state-independent contextuality requires 13 rays
title Quantum state-independent contextuality requires 13 rays
spellingShingle Quantum state-independent contextuality requires 13 rays
Cabello Quintero, Adán
Quantum contextuality
Kochen–Specker theorem
Graph theory
foundations of quantum physics
title_short Quantum state-independent contextuality requires 13 rays
title_full Quantum state-independent contextuality requires 13 rays
title_fullStr Quantum state-independent contextuality requires 13 rays
title_full_unstemmed Quantum state-independent contextuality requires 13 rays
title_sort Quantum state-independent contextuality requires 13 rays
dc.creator.none.fl_str_mv Cabello Quintero, Adán
Kleinmann, Matthias
Portillo Fernández, José Ramón
author Cabello Quintero, Adán
author_facet Cabello Quintero, Adán
Kleinmann, Matthias
Portillo Fernández, José Ramón
author_role author
author2 Kleinmann, Matthias
Portillo Fernández, José Ramón
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Física Aplicada II
FQM-164: Matemática Discreta: Teoría de Grafos y Geometría Computacional
FQM-239: Fundamentos de Mecánica Cuántica
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Quantum contextuality
Kochen–Specker theorem
Graph theory
foundations of quantum physics
topic Quantum contextuality
Kochen–Specker theorem
Graph theory
foundations of quantum physics
description We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three (2012 Phys. Rev. Lett. 108 030402) is actually the minimal set in quantum theory. This contrasts with the case of Kochen–Specker sets, where the smallest set occurs in dimension four.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/135955
https://doi.org/10.1088/1751-8113/49/38/38LT01
url https://hdl.handle.net/11441/135955
https://doi.org/10.1088/1751-8113/49/38/38LT01
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Physics A: Mathematical and Theoretical, 49 (38), 38LT01-1-38LT01-9.
FIS2014-60843-P
https://iopscience.iop.org/article/10.1088/1751-8113/49/38/38LT01
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 IOP Science
publisher.none.fl_str_mv IOP Science
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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score 15,301603

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