Entanglement in fermion systems

Autores
Gigena, Nicolás Alejandro; Rossignoli, Raúl
Año de publicación
2015
Idioma
español castellano
Tipo de recurso
artículo
Estado
versión publicada
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.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Fermion systems
quantum entanglement
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/75315

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repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Entanglement in fermion systemsGigena, Nicolás AlejandroRossignoli, RaúlCiencias ExactasFermion 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.Facultad de Ciencias Exactas2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/75315spainfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:45:10Zoai:sedici.unlp.edu.ar:10915/75315Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:45:10.536SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Entanglement in fermion systems
title Entanglement in fermion systems
spellingShingle Entanglement in fermion systems
Gigena, Nicolás Alejandro
Ciencias Exactas
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
author Gigena, Nicolás Alejandro
author_facet Gigena, Nicolás Alejandro
Rossignoli, Raúl
author_role author
author2 Rossignoli, Raúl
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Fermion systems
quantum entanglement
topic Ciencias Exactas
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.
Facultad de Ciencias Exactas
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
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info:eu-repo/semantics/publishedVersion
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dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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