Polynomial Bell Inequalities
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30394 |
Resumo: | It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell’s theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks |
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Araújo, Rafael Chaves Souto2020-10-13T15:19:29Z2020-10-13T15:19:29Z2016-01-07CHAVES, Rafael. Polynomial Bell Inequalities. Physical Review Letters, [S.L.], v. 116, n. 1, p. 010402, 7 jan. 2016. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.010402. Acesso em: 01 out. 2020. http://dx.doi.org/10.1103/physrevlett.116.010402.0031-900710.1103/physrevlett.116.0104021079-7114https://repositorio.ufrn.br/handle/123456789/30394American Physical SocietyNetwork structureQuantum nonlocalityPolynomial Bell Inequalitiesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleIt is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell’s theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networksengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNinfo:eu-repo/semantics/openAccessORIGINALPolynomialBellInequalities_ARAUJO_2016.pdfPolynomialBellInequalities_ARAUJO_2016.pdfArtigoapplication/pdf251039https://repositorio.ufrn.br/bitstream/123456789/30394/1/PolynomialBellInequalities_ARAUJO_2016.pdf75ed1f548fdf396c2a1e39760a3b8470MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30394/2/license.txte9597aa2854d128fd968be5edc8a28d9MD52TEXTPolynomialBellInequalities_ARAUJO_2016.pdf.txtPolynomialBellInequalities_ARAUJO_2016.pdf.txtExtracted texttext/plain29246https://repositorio.ufrn.br/bitstream/123456789/30394/3/PolynomialBellInequalities_ARAUJO_2016.pdf.txt00c380208b1c4ab5feb6b5a0387d46abMD53THUMBNAILPolynomialBellInequalities_ARAUJO_2016.pdf.jpgPolynomialBellInequalities_ARAUJO_2016.pdf.jpgGenerated Thumbnailimage/jpeg1698https://repositorio.ufrn.br/bitstream/123456789/30394/4/PolynomialBellInequalities_ARAUJO_2016.pdf.jpgb722c00e01fbe37e1be78c8e972af4abMD54123456789/303942020-10-18 04:53:51.315oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-10-18T07:53:51Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Polynomial Bell Inequalities |
title |
Polynomial Bell Inequalities |
spellingShingle |
Polynomial Bell Inequalities Araújo, Rafael Chaves Souto Network structure Quantum nonlocality |
title_short |
Polynomial Bell Inequalities |
title_full |
Polynomial Bell Inequalities |
title_fullStr |
Polynomial Bell Inequalities |
title_full_unstemmed |
Polynomial Bell Inequalities |
title_sort |
Polynomial Bell Inequalities |
author |
Araújo, Rafael Chaves Souto |
author_facet |
Araújo, Rafael Chaves Souto |
author_role |
author |
dc.contributor.author.fl_str_mv |
Araújo, Rafael Chaves Souto |
dc.subject.por.fl_str_mv |
Network structure Quantum nonlocality |
topic |
Network structure Quantum nonlocality |
description |
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell’s theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-01-07 |
dc.date.accessioned.fl_str_mv |
2020-10-13T15:19:29Z |
dc.date.available.fl_str_mv |
2020-10-13T15:19:29Z |
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.citation.fl_str_mv |
CHAVES, Rafael. Polynomial Bell Inequalities. Physical Review Letters, [S.L.], v. 116, n. 1, p. 010402, 7 jan. 2016. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.010402. Acesso em: 01 out. 2020. http://dx.doi.org/10.1103/physrevlett.116.010402. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30394 |
dc.identifier.issn.none.fl_str_mv |
0031-9007 10.1103/physrevlett.116.010402 1079-7114 |
identifier_str_mv |
CHAVES, Rafael. Polynomial Bell Inequalities. Physical Review Letters, [S.L.], v. 116, n. 1, p. 010402, 7 jan. 2016. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.010402. Acesso em: 01 out. 2020. http://dx.doi.org/10.1103/physrevlett.116.010402. 0031-9007 10.1103/physrevlett.116.010402 1079-7114 |
url |
https://repositorio.ufrn.br/handle/123456789/30394 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
dc.source.none.fl_str_mv |
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Universidade Federal do Rio Grande do Norte (UFRN) |
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UFRN |
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UFRN |
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Repositório Institucional da UFRN |
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