The lattice of trumping majorization for 4D probability vectors and 2D catalysts

Autores
Bosyk, Gustavo Martín; Freytes Solari, Héctor Carlos; Bellomo, Guido; Sergioli, Giuseppe
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
Facultad de Ciencias Exactas
Instituto de Física La Plata
Materia
Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/97858
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/97858
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling The lattice of trumping majorization for 4D probability vectors and 2D catalystsBosyk, Gustavo MartínFreytes Solari, Héctor CarlosBellomo, GuidoSergioli, GiuseppeCiencias ExactasFísicaLocal operations and classical communicationEntanglement-assisted transformationsTrumping majorizationLatticeThe transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.Facultad de Ciencias ExactasInstituto de Física La Plata2018-12info: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/10915/97858enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/95925info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-018-21947-0info:eu-repo/semantics/altIdentifier/issn/2045-2322info:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-018-21947-0info:eu-repo/semantics/altIdentifier/hdl/11336/95925info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:01:06Zoai:sedici.unlp.edu.ar:10915/97858Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:01:06.718SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title The lattice of trumping majorization for 4D probability vectors and 2D catalysts
spellingShingle The lattice of trumping majorization for 4D probability vectors and 2D catalysts
Bosyk, Gustavo Martín
Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
title_short The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_full The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_fullStr The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_full_unstemmed The lattice of trumping majorization for 4D probability vectors and 2D catalysts
title_sort The lattice of trumping majorization for 4D probability vectors and 2D catalysts
dc.creator.none.fl_str_mv Bosyk, Gustavo Martín
Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
author Bosyk, Gustavo Martín
author_facet Bosyk, Gustavo Martín
Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
author_role author
author2 Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
author2_role author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
topic Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
dc.description.none.fl_txt_mv The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
Facultad de Ciencias Exactas
Instituto de Física La Plata
description The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
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/10915/97858
url http://sedici.unlp.edu.ar/handle/10915/97858
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/95925
info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-018-21947-0
info:eu-repo/semantics/altIdentifier/issn/2045-2322
info:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-018-21947-0
info:eu-repo/semantics/altIdentifier/hdl/11336/95925
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 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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