Genuine-multipartite entanglement criteria based on positive maps

Fabien Clivaz, Marcus Huber, Ludovico Lami, Gláucia Murta

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)


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.

Original languageEnglish
Article number082201
JournalJournal of Mathematical Physics
Issue number8
Publication statusPublished - 2017


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