Genuine-multipartite entanglement criteria based on positive maps

TL;DR

This paper introduces a novel method using non-positive maps to detect genuine multipartite entanglement, overcoming limitations of traditional positive map techniques in multipartite quantum systems.

Contribution

It generalizes bipartite positive map criteria to multipartite systems by constructing non-positive maps that identify genuine multipartite entanglement.

Findings

Constructed explicit examples of multipartite non-positive maps

Demonstrated robustness in detecting genuine multipartite entanglement

Extended the applicability of positive map techniques to complex quantum states

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 bi-separable 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.