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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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v8_n1_p_Bosyk http://hdl.handle.net/20.500.12110/paper_20452322_v8_n1_p_Bosyk |
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paper:paper_20452322_v8_n1_p_Bosyk2023-06-08T16:33:33Z The lattice of trumping majorization for 4D probability vectors and 2D catalysts 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). 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v8_n1_p_Bosyk 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 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). |
| 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 |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20452322_v8_n1_p_Bosyk http://hdl.handle.net/20.500.12110/paper_20452322_v8_n1_p_Bosyk |
| _version_ |
1768544387424321536 |