LOCC convertibility of entangled states in infinite-dimensional systems

Autores
Massri, César; Bellomo, Guido; Freytes, Hector; Giuntini, Roberto; Sergioli, Giuseppe; Bosyk, Gustavo Martín
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem.
Instituto de Física La Plata
Materia
Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
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:10915/167383
Acceder
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network_name_str SEDICI (UNLP)
spelling LOCC convertibility of entangled states in infinite-dimensional systemsMassri, CésarBellomo, GuidoFreytes, HectorGiuntini, RobertoSergioli, GiuseppeBosyk, Gustavo MartínFísicaentanglementLOCC convertibilitymajorization latticecommon resourcesinfinite dimensionWe advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem.Instituto de Física La Plata2024info: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/10915/167383enginfo:eu-repo/semantics/altIdentifier/issn/1367-2630info:eu-repo/semantics/altIdentifier/doi/10.1088/1367-2630/ad503dinfo: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:UNLP2025-10-22T17:25:28Zoai:sedici.unlp.edu.ar:10915/167383Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:25:28.815SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv LOCC convertibility of entangled states in infinite-dimensional systems
title LOCC convertibility of entangled states in infinite-dimensional systems
spellingShingle LOCC convertibility of entangled states in infinite-dimensional systems
Massri, César
Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
title_short LOCC convertibility of entangled states in infinite-dimensional systems
title_full LOCC convertibility of entangled states in infinite-dimensional systems
title_fullStr LOCC convertibility of entangled states in infinite-dimensional systems
title_full_unstemmed LOCC convertibility of entangled states in infinite-dimensional systems
title_sort LOCC convertibility of entangled states in infinite-dimensional systems
dc.creator.none.fl_str_mv Massri, César
Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
author Massri, César
author_facet Massri, César
Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
author_role author
author2 Bellomo, Guido
Freytes, Hector
Giuntini, Roberto
Sergioli, Giuseppe
Bosyk, Gustavo Martín
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
topic Física
entanglement
LOCC convertibility
majorization lattice
common resources
infinite dimension
dc.description.none.fl_txt_mv We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem.
Instituto de Física La Plata
description We advance on the conversion of bipartite quantum states via local operations and classical communication (LOCC) for infinite-dimensional systems. We introduce δ-LOCC convertibility based on the observation that any pure state can be approximated by a state with finite-support Schmidt coefficients. We show that δ-LOCC convertibility of bipartite states is fully characterized by a majorization relation between the sequences of squared Schmidt coefficients, providing a novel extension of Nielsen’s theorem for infinite-dimensional systems. Hence, our definition is equivalent to the one of ϵ-LOCC convertibility (Owari et al 2008 Quantum Inf. Comput. 8 0030), but deals with states having finitely supported sequences of Schmidt coefficients. Additionally, we discuss the notions of optimal common resource and optimal common product in this scenario. The optimal common product always exists, whereas the optimal common resource depends on the existence of a common resource. This highlights a distinction between the resource-theoretic aspects of finite versus infinite-dimensional systems. Our results rely on the order-theoretic properties of majorization for infinite sequences, applicable beyond the LOCC convertibility problem.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/167383
url http://sedici.unlp.edu.ar/handle/10915/167383
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1367-2630
info:eu-repo/semantics/altIdentifier/doi/10.1088/1367-2630/ad503d
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
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution 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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