Detecting entanglement harnessing Lindblad structure

TL;DR

This paper introduces a new class of positive maps derived from Lindblad structures to improve entanglement detection, generalizing known maps and proposing a measure for genuine multipartite entanglement.

Contribution

It provides a generic method to construct positive maps from Lindblad structures, unifies known maps like transposition and Choi map, and extends entanglement detection techniques.

Findings

Derived positive maps from Lindblad structures.

Unified transposition and Choi map within this framework.

Proposed a measure for genuine multipartite entanglement.

Abstract

The problem of entanglement detection is a long standing problem in quantum information theory. One of the primary procedures of detecting entanglement is to find the suitable positive but non-completely positive maps. Here we try to give a generic prescription to construct a positive map that can be useful for such scenarios. We study a class of positive maps arising from Lindblad structures. We show that two famous positive maps viz. transposition and Choi map can be obtained as a special case of a class of positive maps having Lindblad structure. Generalizing the transposition map to a one parameter family we have used it to detect genuine multipartite entanglement. Finally being motivated by the negativity of entanglement, we have defined a similar measure for genuine multipartite entanglement.