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

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...

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Autores principales: Bosyk, Gustavo Martín, Freytes Solari, Héctor Carlos, Bellomo, Guido, Sergioli, Giuseppe
Formato: Articulo
Lenguaje:Inglés
Publicado: 2018
Materias:
Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/97858
https://ri.conicet.gov.ar/11336/95925
https://www.nature.com/articles/s41598-018-21947-0
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-97858
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
spellingShingle Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
Bosyk, Gustavo Martín
Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
The lattice of trumping majorization for 4D probability vectors and 2D catalysts
topic_facet Ciencias Exactas
Física
Local operations and classical communication
Entanglement-assisted transformations
Trumping majorization
Lattice
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.
format Articulo
Articulo
author Bosyk, Gustavo Martín
Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
author_facet Bosyk, Gustavo Martín
Freytes Solari, Héctor Carlos
Bellomo, Guido
Sergioli, Giuseppe
author_sort Bosyk, Gustavo Martín
title The lattice of trumping majorization for 4D probability vectors and 2D catalysts
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 lattice of trumping majorization for 4d probability vectors and 2d catalysts
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/97858
https://ri.conicet.gov.ar/11336/95925
https://www.nature.com/articles/s41598-018-21947-0
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