Fermionic entanglement in superconducting systems

Autores
Di Tullio, Marco; Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.
Fil: Di Tullio, Marco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Gigena, Nicolás Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Materia
Entanglement
Fermionic
Entropy
Superconductor
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:11336/100997
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/100997
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Fermionic entanglement in superconducting systemsDi Tullio, MarcoGigena, Nicolás AlejandroRossignoli, Raúl DanteEntanglementFermionicEntropySuperconductorhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.Fil: Di Tullio, Marco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Gigena, Nicolás Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaAmerican Physical Society2018-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/100997Di Tullio, Marco; Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante; Fermionic entanglement in superconducting systems; American Physical Society; Physical Review A; 97; 6; 6-2018; 621091-62109122469-9926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062109info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.97.062109info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:30:41Zoai:ri.conicet.gov.ar:11336/100997instacron: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:34982025-09-29 10:30:41.45CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Fermionic entanglement in superconducting systems
title Fermionic entanglement in superconducting systems
spellingShingle Fermionic entanglement in superconducting systems
Di Tullio, Marco
Entanglement
Fermionic
Entropy
Superconductor
title_short Fermionic entanglement in superconducting systems
title_full Fermionic entanglement in superconducting systems
title_fullStr Fermionic entanglement in superconducting systems
title_full_unstemmed Fermionic entanglement in superconducting systems
title_sort Fermionic entanglement in superconducting systems
dc.creator.none.fl_str_mv Di Tullio, Marco
Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author Di Tullio, Marco
author_facet Di Tullio, Marco
Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author_role author
author2 Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author2_role author
author
dc.subject.none.fl_str_mv Entanglement
Fermionic
Entropy
Superconductor
topic Entanglement
Fermionic
Entropy
Superconductor
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 examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.
Fil: Di Tullio, Marco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Gigena, Nicolás Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
description We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.
publishDate 2018
dc.date.none.fl_str_mv 2018-06
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/11336/100997
Di Tullio, Marco; Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante; Fermionic entanglement in superconducting systems; American Physical Society; Physical Review A; 97; 6; 6-2018; 621091-6210912
2469-9926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/100997
identifier_str_mv Di Tullio, Marco; Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante; Fermionic entanglement in superconducting systems; American Physical Society; Physical Review A; 97; 6; 6-2018; 621091-6210912
2469-9926
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/pra/abstract/10.1103/PhysRevA.97.062109
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.97.062109
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
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
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score 13.069144

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