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
- 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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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 |
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reponame:CIC Digital (CICBA) instname:Comisión de Investigaciones Científicas de la Provincia de Buenos Aires instacron:CICBA |
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Comisión de Investigaciones Científicas de la Provincia de Buenos Aires |
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CICBA |
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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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