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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Detalles Bibliográficos
Autores principales:	Bosyk, G.M., Freytes, H., Bellomo, G., Sergioli, G.
Formato:	JOUR
Materias:	article catalyst entropy probability
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_20452322_v8_n1_p_Bosyk
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_20452322_v8_n1_p_Bosyk
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spelling	todo:paper_20452322_v8_n1_p_Bosyk2023-10-03T16:38:22Z The lattice of trumping majorization for 4D probability vectors and 2D catalysts Bosyk, G.M. Freytes, H. Bellomo, G. Sergioli, G. article catalyst entropy probability 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. © 2018 The Author(s). JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_20452322_v8_n1_p_Bosyk
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	article catalyst entropy probability
spellingShingle	article catalyst entropy probability Bosyk, G.M. Freytes, H. Bellomo, G. Sergioli, G. The lattice of trumping majorization for 4D probability vectors and 2D catalysts
topic_facet	article catalyst entropy probability
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. © 2018 The Author(s).
format	JOUR
author	Bosyk, G.M. Freytes, H. Bellomo, G. Sergioli, G.
author_facet	Bosyk, G.M. Freytes, H. Bellomo, G. Sergioli, G.
author_sort	Bosyk, G.M.
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
url	http://hdl.handle.net/20.500.12110/paper_20452322_v8_n1_p_Bosyk
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The lattice of trumping majorization for 4D probability vectors and 2D catalysts

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