Genuine-multipartite entanglement criteria based on positive maps

Fabien Clivaz, Marcus Huber, Ludovico Lami, Gláucia Murta

    Research output: Contribution to journalArticleResearchpeer-review

    10 Citations (Scopus)

    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.
    Original languageEnglish
    Article number082201
    JournalJournal of Mathematical Physics
    Volume58
    Issue number8
    DOIs
    Publication statusPublished - 1 Aug 2017

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