Genuine-multipartite entanglement criteria based on positive maps

TitleGenuine-multipartite entanglement criteria based on positive maps
Publication TypeJournal Article
Year of Publication2017
AuthorsClivaz, F, Huber, M, Lami, L, Murta, G
JournalJOURNAL OF MATHEMATICAL PHYSICS
Volume58
Issue8
Date Publishedaug
ISSN0022-2488
Abstract

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way. Published by AIP Publishing.

DOI10.1063/1.4998433
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