Entanglement and distillation from symmetric positive maps

TL;DR

This paper unifies and extends symmetric positive maps for entanglement detection, introducing new methods that improve detection capabilities, including multipartite entanglement witnesses and detection of states with local positive partial transposition.

Contribution

It generalizes the reduction map and develops a new family of positive maps, enhancing entanglement detection techniques using multiple copies and local filters.

Findings

Expanded detection of entangled states with local positive partial transposition

Construction of multipartite entanglement witnesses from positive maps

Enhanced detection capabilities through generalized reduction maps

Abstract

Recently, a toolkit of highly symmetric techniques employing matrix inequalities has been developed to detect entanglement in various ways. Here we unifiedly explain in detail these methods, and expand them to a new family of positive maps with further detection capabilities. In the simplest case, we generalize the reduction map to detect more generic states using both multiple copies and local filters. Through the Choi-Jamio{\l}kowski isomorphism, this family of maps leads to a construction of multipartite entanglement witnesses. Discussions and examples are provided regarding the detection of states with local positive partial transposition and the use of multiple copies.