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 M., Freytes, Hector, Bellomo, Guido, Sergioli, Giuseppe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5829238/
https://www.ncbi.nlm.nih.gov/pubmed/29487363
http://dx.doi.org/10.1038/s41598-018-21947-0
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author Bosyk, Gustavo M.
Freytes, Hector
Bellomo, Guido
Sergioli, Giuseppe
author_facet Bosyk, Gustavo M.
Freytes, Hector
Bellomo, Guido
Sergioli, Giuseppe
author_sort Bosyk, Gustavo M.
collection PubMed
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.
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spelling pubmed-58292382018-03-01 The lattice of trumping majorization for 4D probability vectors and 2D catalysts Bosyk, Gustavo M. Freytes, Hector Bellomo, Guido Sergioli, Giuseppe Sci Rep Article 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. Nature Publishing Group UK 2018-02-27 /pmc/articles/PMC5829238/ /pubmed/29487363 http://dx.doi.org/10.1038/s41598-018-21947-0 Text en © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Bosyk, Gustavo M.
Freytes, Hector
Bellomo, Guido
Sergioli, Giuseppe
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
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_short 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
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5829238/
https://www.ncbi.nlm.nih.gov/pubmed/29487363
http://dx.doi.org/10.1038/s41598-018-21947-0
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