Entanglement in fermion systems

Autores
Gigena, Nicolás Alejandro; Rossignoli, Raúl Dante
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión enviada
Descripción
We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert spaceHis defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases ofHis a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined in [J. Schliemann et al, Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement . It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that of the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy are evaluated analytically, extending the results of previous ref. to general states.
Materia
Ingenierías y Tecnologías
Fermion systems
quantum entanglement
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
CIC Digital (CICBA)
Institución
Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
OAI Identificador
oai:digital.cic.gba.gob.ar:11746/10007

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network_acronym_str CICBA
repository_id_str 9441
network_name_str CIC Digital (CICBA)
spelling Entanglement in fermion systemsGigena, Nicolás AlejandroRossignoli, Raúl DanteIngenierías y TecnologíasFermion systemsquantum entanglementWe analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert spaceHis defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases ofHis a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined in [J. Schliemann et al, Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement . It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that of the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy are evaluated analytically, extending the results of previous ref. to general states.2015-10-23info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttps://digital.cic.gba.gob.ar/handle/11746/10007enginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.92.042326info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/reponame:CIC Digital (CICBA)instname:Comisión de Investigaciones Científicas de la Provincia de Buenos Airesinstacron:CICBA2025-09-04T09:43:08Zoai:digital.cic.gba.gob.ar:11746/10007Institucionalhttp://digital.cic.gba.gob.arOrganismo científico-tecnológicoNo correspondehttp://digital.cic.gba.gob.ar/oai/snrdmarisa.degiusti@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:94412025-09-04 09:43:08.38CIC Digital (CICBA) - Comisión de Investigaciones Científicas de la Provincia de Buenos Airesfalse
dc.title.none.fl_str_mv Entanglement in fermion systems
title Entanglement in fermion systems
spellingShingle Entanglement in fermion systems
Gigena, Nicolás Alejandro
Ingenierías y Tecnologías
Fermion systems
quantum entanglement
title_short Entanglement in fermion systems
title_full Entanglement in fermion systems
title_fullStr Entanglement in fermion systems
title_full_unstemmed Entanglement in fermion systems
title_sort Entanglement in fermion systems
dc.creator.none.fl_str_mv Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author Gigena, Nicolás Alejandro
author_facet Gigena, Nicolás Alejandro
Rossignoli, Raúl Dante
author_role author
author2 Rossignoli, Raúl Dante
author2_role author
dc.subject.none.fl_str_mv Ingenierías y Tecnologías
Fermion systems
quantum entanglement
topic Ingenierías y Tecnologías
Fermion systems
quantum entanglement
dc.description.none.fl_txt_mv We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert spaceHis defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases ofHis a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined in [J. Schliemann et al, Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement . It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that of the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy are evaluated analytically, extending the results of previous ref. to general states.
description We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert spaceHis defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases ofHis a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined in [J. Schliemann et al, Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement . It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that of the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy are evaluated analytically, extending the results of previous ref. to general states.
publishDate 2015
dc.date.none.fl_str_mv 2015-10-23
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://digital.cic.gba.gob.ar/handle/11746/10007
url https://digital.cic.gba.gob.ar/handle/11746/10007
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.92.042326
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:CIC Digital (CICBA)
instname:Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
instacron:CICBA
reponame_str CIC Digital (CICBA)
collection CIC Digital (CICBA)
instname_str Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
instacron_str CICBA
institution CICBA
repository.name.fl_str_mv CIC Digital (CICBA) - Comisión de Investigaciones Científicas de la Provincia de Buenos Aires
repository.mail.fl_str_mv marisa.degiusti@sedici.unlp.edu.ar
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