Detecting entanglement harnessing Lindblad structure

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, reduction map 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.

Automated summary

This article investigates the problem of entanglement detection in quantum information theory, particularly focusing on constructing suitable mappings for non-completely positive maps. The study presents a class of positive maps derived from Lindblad structures, showing that famous positive maps such as transposition, reduction map, and Choi map can be obtained as special cases within this class. By generalizing the transposition map, the authors successfully detect genuine multipartite entanglement and define a similar measure to assess it.