Genuine-multipartite entanglement criteria based on positive maps

Journal article (2017)

Authors

Fabien Clivaz Université de Genève
Marcus Huber Austrian Academy of Sciences
Ludovico Lami Universitat Autònoma de Barcelona
G. Murta Guimarães Universidade Federal de Minas Gerais, QuTech Advanced Research Centre, QID/Wehner Group - QuTech Advanced Research Centre
Research Group
QID/Wehner Group (QuTech Advanced Research Centre) (TU Delft)
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Published Date

2017

Language

English

Reuse Rights

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Faculty

QuTech Advanced Research Centre

Department

Quantum Internet Division

Research Group

QID/Wehner Group

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.