Witnessing genuine multipartite entanglement with positive maps

TL;DR

This paper introduces a unified framework linking positive maps to entanglement witnesses, enabling improved detection of genuine multipartite entanglement, especially in complex bound entangled states, surpassing previous methods.

Contribution

It develops a general method connecting positive maps with witnesses for partial separability, enhancing detection capabilities in multipartite quantum systems.

Findings

New witness detects genuine multipartite entanglement in bound entangled states

Framework outperforms previous criteria in higher dimensions

Demonstrates connection between positive maps and entanglement detection

Abstract

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by non-decomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.