Wigner separability entropy and complexity of quantum dynamics

Autores
Benenti, Giuliano; Carlo, Gabriel Gustavo; Prosen, Toma
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase-space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms. © 2012 American Physical Society.
Fil: Benenti, Giuliano. Istituto Nazionale di Fisica Nucleare; Italia. Università degli Studi dell'Insubria; Italia
Fil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Prosen, Toma. Universidad de Ljubljana; Eslovenia
Materia
Separability entropy
Quantum complexity
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:11336/196252
Acceder
id CONICETDig_63d16d2501c537e0e75c4284aec34752
oai_identifier_str oai:ri.conicet.gov.ar:11336/196252
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Wigner separability entropy and complexity of quantum dynamicsBenenti, GiulianoCarlo, Gabriel GustavoProsen, TomaSeparability entropyQuantum complexityhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase-space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms. © 2012 American Physical Society.Fil: Benenti, Giuliano. Istituto Nazionale di Fisica Nucleare; Italia. Università degli Studi dell'Insubria; ItaliaFil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Prosen, Toma. Universidad de Ljubljana; EsloveniaAmerican Physical Society2012-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/196252Benenti, Giuliano; Carlo, Gabriel Gustavo; Prosen, Toma; Wigner separability entropy and complexity of quantum dynamics; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 85; 5; 5-2012; 1-61063-651X1095-3787CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.051129info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.85.051129info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1201.2196info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:30Zoai:ri.conicet.gov.ar:11336/196252instacron: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 10:01:30.867CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Wigner separability entropy and complexity of quantum dynamics
title Wigner separability entropy and complexity of quantum dynamics
spellingShingle Wigner separability entropy and complexity of quantum dynamics
Benenti, Giuliano
Separability entropy
Quantum complexity
title_short Wigner separability entropy and complexity of quantum dynamics
title_full Wigner separability entropy and complexity of quantum dynamics
title_fullStr Wigner separability entropy and complexity of quantum dynamics
title_full_unstemmed Wigner separability entropy and complexity of quantum dynamics
title_sort Wigner separability entropy and complexity of quantum dynamics
dc.creator.none.fl_str_mv Benenti, Giuliano
Carlo, Gabriel Gustavo
Prosen, Toma
author Benenti, Giuliano
author_facet Benenti, Giuliano
Carlo, Gabriel Gustavo
Prosen, Toma
author_role author
author2 Carlo, Gabriel Gustavo
Prosen, Toma
author2_role author
author
dc.subject.none.fl_str_mv Separability entropy
Quantum complexity
topic Separability entropy
Quantum complexity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase-space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms. © 2012 American Physical Society.
Fil: Benenti, Giuliano. Istituto Nazionale di Fisica Nucleare; Italia. Università degli Studi dell'Insubria; Italia
Fil: Carlo, Gabriel Gustavo. Comisión Nacional de Energía Atómica. Gerencia de Área Investigaciones y Aplicaciones No Nucleares. Gerencia Física (CAC). Departamento de Física de la Materia Condensada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Prosen, Toma. Universidad de Ljubljana; Eslovenia
description We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase-space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms. © 2012 American Physical Society.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
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/11336/196252
Benenti, Giuliano; Carlo, Gabriel Gustavo; Prosen, Toma; Wigner separability entropy and complexity of quantum dynamics; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 85; 5; 5-2012; 1-6
1063-651X
1095-3787
CONICET Digital
CONICET
url http://hdl.handle.net/11336/196252
identifier_str_mv Benenti, Giuliano; Carlo, Gabriel Gustavo; Prosen, Toma; Wigner separability entropy and complexity of quantum dynamics; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 85; 5; 5-2012; 1-6
1063-651X
1095-3787
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.051129
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.85.051129
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1201.2196
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
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
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
_version_ 1842269700315152384
score 13.13397

Publicaciones similares