One-body entanglement as a quantum resource in fermionic systems

We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hu...

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Autores: Gigena, Nicolás Alejandro, Di Tullio, Marco, Rossignoli, Raúl Dante
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/125547
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/125547
Access Level:acceso abierto
Palabra clave:Ciencias Exactas
Física
Entanglement entropy
Entanglement measures
Fermions
Quantum computation
Quantum entanglement
Resource theories
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spelling One-body entanglement as a quantum resource in fermionic systemsGigena, Nicolás AlejandroDi Tullio, MarcoRossignoli, Raúl DanteCiencias ExactasFísicaEntanglement entropyEntanglement measuresFermionsQuantum computationQuantum entanglementResource theoriesWe show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure N-fermion state, from which the SPDM [together with the (N-1)-body density matrix] can be derived. It is then proved that under FLO operations the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.Facultad de Ciencias ExactasInstituto de Física La Plata2020-10info: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/10915/125547enginfo:eu-repo/semantics/altIdentifier/issn/2469-9926info:eu-repo/semantics/altIdentifier/issn/2469-9934info:eu-repo/semantics/altIdentifier/arxiv/2001.03570info:eu-repo/semantics/altIdentifier/doi/10.1103/physreva.102.042410info: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:UNLP2024-05-08T13:08:04Zoai:sedici.unlp.edu.ar:10915/125547Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292024-05-08 13:08:05.248SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv One-body entanglement as a quantum resource in fermionic systems
title One-body entanglement as a quantum resource in fermionic systems
spellingShingle One-body entanglement as a quantum resource in fermionic systems
Gigena, Nicolás Alejandro
Ciencias Exactas
Física
Entanglement entropy
Entanglement measures
Fermions
Quantum computation
Quantum entanglement
Resource theories
title_short One-body entanglement as a quantum resource in fermionic systems
title_full One-body entanglement as a quantum resource in fermionic systems
title_fullStr One-body entanglement as a quantum resource in fermionic systems
title_full_unstemmed One-body entanglement as a quantum resource in fermionic systems
title_sort One-body entanglement as a quantum resource in fermionic systems
dc.creator.none.fl_str_mv Gigena, Nicolás Alejandro
Di Tullio, Marco
Rossignoli, Raúl Dante
author Gigena, Nicolás Alejandro
author_facet Gigena, Nicolás Alejandro
Di Tullio, Marco
Rossignoli, Raúl Dante
author_role author
author2 Di Tullio, Marco
Rossignoli, Raúl Dante
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Física
Entanglement entropy
Entanglement measures
Fermions
Quantum computation
Quantum entanglement
Resource theories
topic Ciencias Exactas
Física
Entanglement entropy
Entanglement measures
Fermions
Quantum computation
Quantum entanglement
Resource theories
description We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure N-fermion state, from which the SPDM [together with the (N-1)-body density matrix] can be derived. It is then proved that under FLO operations the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.
publishDate 2020
dc.date.none.fl_str_mv 2020-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/125547
url http://sedici.unlp.edu.ar/handle/10915/125547
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/2469-9926
info:eu-repo/semantics/altIdentifier/issn/2469-9934
info:eu-repo/semantics/altIdentifier/arxiv/2001.03570
info:eu-repo/semantics/altIdentifier/doi/10.1103/physreva.102.042410
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
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)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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