Problem of quantifying quantum correlations with non-commutative discord

Autores
Majtey, Ana Paula; Bussandri, Diego G.; Osán, Tristán Martín; Lamberti, Pedro Walter; Valdés-Hernández, A.
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.
Fil: Majtey, Ana Paula. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina
Fil: Bussandri, Diego G.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Lamberti, Pedro Walter. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Valdés-Hernández, A.. Universidad Nacional Autonoma de Mexico. Facultad de Ciencias; México
Materia
Bipartite Systems
Hilbert&Ndash;Schmidt Norm
Non-Commutative Discord
Quantum Correlations
Quantum Correlations Measure
Quantum Discord
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/63765
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/63765
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Problem of quantifying quantum correlations with non-commutative discordMajtey, Ana PaulaBussandri, Diego G.Osán, Tristán MartínLamberti, Pedro WalterValdés-Hernández, A.Bipartite SystemsHilbert&Ndash;Schmidt NormNon-Commutative DiscordQuantum CorrelationsQuantum Correlations MeasureQuantum Discordhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.Fil: Majtey, Ana Paula. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; ArgentinaFil: Bussandri, Diego G.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Lamberti, Pedro Walter. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Valdés-Hernández, A.. Universidad Nacional Autonoma de Mexico. Facultad de Ciencias; MéxicoSpringer2017-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63765Majtey, Ana Paula; Bussandri, Diego G.; Osán, Tristán Martín; Lamberti, Pedro Walter; Valdés-Hernández, A.; Problem of quantifying quantum correlations with non-commutative discord; Springer; Quantum Information Processing; 16; 9; 9-20171570-07551573-1332CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11128-017-1669-9info:eu-repo/semantics/altIdentifier/doi/10.1007/s11128-017-1669-9info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:46:34Zoai:ri.conicet.gov.ar:11336/63765instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:46:34.842CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Problem of quantifying quantum correlations with non-commutative discord
title Problem of quantifying quantum correlations with non-commutative discord
spellingShingle Problem of quantifying quantum correlations with non-commutative discord
Majtey, Ana Paula
Bipartite Systems
Hilbert&Ndash;Schmidt Norm
Non-Commutative Discord
Quantum Correlations
Quantum Correlations Measure
Quantum Discord
title_short Problem of quantifying quantum correlations with non-commutative discord
title_full Problem of quantifying quantum correlations with non-commutative discord
title_fullStr Problem of quantifying quantum correlations with non-commutative discord
title_full_unstemmed Problem of quantifying quantum correlations with non-commutative discord
title_sort Problem of quantifying quantum correlations with non-commutative discord
dc.creator.none.fl_str_mv Majtey, Ana Paula
Bussandri, Diego G.
Osán, Tristán Martín
Lamberti, Pedro Walter
Valdés-Hernández, A.
author Majtey, Ana Paula
author_facet Majtey, Ana Paula
Bussandri, Diego G.
Osán, Tristán Martín
Lamberti, Pedro Walter
Valdés-Hernández, A.
author_role author
author2 Bussandri, Diego G.
Osán, Tristán Martín
Lamberti, Pedro Walter
Valdés-Hernández, A.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Bipartite Systems
Hilbert&Ndash;Schmidt Norm
Non-Commutative Discord
Quantum Correlations
Quantum Correlations Measure
Quantum Discord
topic Bipartite Systems
Hilbert&Ndash;Schmidt Norm
Non-Commutative Discord
Quantum Correlations
Quantum Correlations Measure
Quantum Discord
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.
Fil: Majtey, Ana Paula. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina
Fil: Bussandri, Diego G.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Osán, Tristán Martín. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Lamberti, Pedro Walter. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Valdés-Hernández, A.. Universidad Nacional Autonoma de Mexico. Facultad de Ciencias; México
description In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt’s is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt’s. In addition, the resulting measure inherits the main properties of Guo’s measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo’s measure can result in an overestimation of quantum correlations. However, since Guo’s measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.
publishDate 2017
dc.date.none.fl_str_mv 2017-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/63765
Majtey, Ana Paula; Bussandri, Diego G.; Osán, Tristán Martín; Lamberti, Pedro Walter; Valdés-Hernández, A.; Problem of quantifying quantum correlations with non-commutative discord; Springer; Quantum Information Processing; 16; 9; 9-2017
1570-0755
1573-1332
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63765
identifier_str_mv Majtey, Ana Paula; Bussandri, Diego G.; Osán, Tristán Martín; Lamberti, Pedro Walter; Valdés-Hernández, A.; Problem of quantifying quantum correlations with non-commutative discord; Springer; Quantum Information Processing; 16; 9; 9-2017
1570-0755
1573-1332
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s11128-017-1669-9
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11128-017-1669-9
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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