An algorithm based on negative probabilities for a separability criterion
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s11128-015-1053-6 http://hdl.handle.net/11449/160860 |
Resumo: | Here, we demonstrate that entangled states can be written as separable states [rho(1...N) = Sigma(i), p(i)rho((1))(i) circle times...circle times rho((N))(i), 1 to N refering to the parts and p(i) to the nonnegative probabilities], although for some of the coefficients, p(i) assume negative values, while others are larger than 1 such to keep their sum equal to 1. We recognize this feature as a signature of non-separability or pseudoseparability. We systematize that kind of decomposition through an algorithm for the explicit separation of density matrices, and we apply it to illustrate the separation of some particular bipartite and tripartite states, including a multipartite circle times(N)(2) one-parameter Werner-like state. We also work out an arbitrary bipartite 2 x 2 state and show that in the particular case where this state reduces to an X-type density matrix, our algorithm leads to the separability conditions on the parameters, confirmed by the Peres-Horodecki partial transposition recipe. We finally propose a measure for quantifying the degree of entanglement based on these peculiar negative (and greater than one) probabilities. |
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Repositório Institucional da UNESP |
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An algorithm based on negative probabilities for a separability criterionHere, we demonstrate that entangled states can be written as separable states [rho(1...N) = Sigma(i), p(i)rho((1))(i) circle times...circle times rho((N))(i), 1 to N refering to the parts and p(i) to the nonnegative probabilities], although for some of the coefficients, p(i) assume negative values, while others are larger than 1 such to keep their sum equal to 1. We recognize this feature as a signature of non-separability or pseudoseparability. We systematize that kind of decomposition through an algorithm for the explicit separation of density matrices, and we apply it to illustrate the separation of some particular bipartite and tripartite states, including a multipartite circle times(N)(2) one-parameter Werner-like state. We also work out an arbitrary bipartite 2 x 2 state and show that in the particular case where this state reduces to an X-type density matrix, our algorithm leads to the separability conditions on the parameters, confirmed by the Peres-Horodecki partial transposition recipe. We finally propose a measure for quantifying the degree of entanglement based on these peculiar negative (and greater than one) probabilities.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Reg Cariri, Dept Fis, BR-63010970 Juazeiro Do Norte, BrazilUniv Estadual Paulista, BR-18409010 Itapeva, SP, BrazilUniv Fed Sao Carlos, Dept Fis, BR-13565905 Sao Carlos, SP, BrazilUniv Sao Paulo, Inst Fis Sao Carlos, BR-13560970 Sao Carlos, SP, BrazilCity Univ London, Ctr Math Sci, London EC1V 0HB, EnglandUniv Estadual Paulista, BR-18409010 Itapeva, SP, BrazilSpringerUniv Reg CaririUniversidade Estadual Paulista (Unesp)Universidade Federal de São Carlos (UFSCar)Universidade de São Paulo (USP)City Univ LondonPonte, M. A. de [UNESP]Mizrahi, S. S.Moussa, M. H. Y.2018-11-26T16:17:02Z2018-11-26T16:17:02Z2015-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3351-3366application/pdfhttp://dx.doi.org/10.1007/s11128-015-1053-6Quantum Information Processing. New York: Springer, v. 14, n. 9, p. 3351-3366, 2015.1570-0755http://hdl.handle.net/11449/16086010.1007/s11128-015-1053-6WOS:000361820900012WOS000361820900012.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengQuantum Information Processing0,708info:eu-repo/semantics/openAccess2023-10-14T06:06:52Zoai:repositorio.unesp.br:11449/160860Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-14T06:06:52Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
An algorithm based on negative probabilities for a separability criterion |
title |
An algorithm based on negative probabilities for a separability criterion |
spellingShingle |
An algorithm based on negative probabilities for a separability criterion Ponte, M. A. de [UNESP] |
title_short |
An algorithm based on negative probabilities for a separability criterion |
title_full |
An algorithm based on negative probabilities for a separability criterion |
title_fullStr |
An algorithm based on negative probabilities for a separability criterion |
title_full_unstemmed |
An algorithm based on negative probabilities for a separability criterion |
title_sort |
An algorithm based on negative probabilities for a separability criterion |
author |
Ponte, M. A. de [UNESP] |
author_facet |
Ponte, M. A. de [UNESP] Mizrahi, S. S. Moussa, M. H. Y. |
author_role |
author |
author2 |
Mizrahi, S. S. Moussa, M. H. Y. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Univ Reg Cariri Universidade Estadual Paulista (Unesp) Universidade Federal de São Carlos (UFSCar) Universidade de São Paulo (USP) City Univ London |
dc.contributor.author.fl_str_mv |
Ponte, M. A. de [UNESP] Mizrahi, S. S. Moussa, M. H. Y. |
description |
Here, we demonstrate that entangled states can be written as separable states [rho(1...N) = Sigma(i), p(i)rho((1))(i) circle times...circle times rho((N))(i), 1 to N refering to the parts and p(i) to the nonnegative probabilities], although for some of the coefficients, p(i) assume negative values, while others are larger than 1 such to keep their sum equal to 1. We recognize this feature as a signature of non-separability or pseudoseparability. We systematize that kind of decomposition through an algorithm for the explicit separation of density matrices, and we apply it to illustrate the separation of some particular bipartite and tripartite states, including a multipartite circle times(N)(2) one-parameter Werner-like state. We also work out an arbitrary bipartite 2 x 2 state and show that in the particular case where this state reduces to an X-type density matrix, our algorithm leads to the separability conditions on the parameters, confirmed by the Peres-Horodecki partial transposition recipe. We finally propose a measure for quantifying the degree of entanglement based on these peculiar negative (and greater than one) probabilities. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-09-01 2018-11-26T16:17:02Z 2018-11-26T16:17:02Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s11128-015-1053-6 Quantum Information Processing. New York: Springer, v. 14, n. 9, p. 3351-3366, 2015. 1570-0755 http://hdl.handle.net/11449/160860 10.1007/s11128-015-1053-6 WOS:000361820900012 WOS000361820900012.pdf |
url |
http://dx.doi.org/10.1007/s11128-015-1053-6 http://hdl.handle.net/11449/160860 |
identifier_str_mv |
Quantum Information Processing. New York: Springer, v. 14, n. 9, p. 3351-3366, 2015. 1570-0755 10.1007/s11128-015-1053-6 WOS:000361820900012 WOS000361820900012.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Quantum Information Processing 0,708 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
3351-3366 application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1797789392814735360 |