Construction of a Family of Positive But Not Completely Positive Map For the Detection of Bound Entangled States

TL;DR

This paper introduces a new family of positive but not completely positive maps, useful for detecting bound entangled states and states with negative partial transpose, advancing quantum entanglement detection methods.

Contribution

The paper constructs a novel family of maps that are positive but not completely positive, specifically designed for entanglement detection in quantum states.

Findings

Constructed a family of positive but not completely positive maps.

Demonstrated the maps' effectiveness in detecting bound entangled states.

Showed the maps can identify states with negative partial transpose.

Abstract

We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of bound entangled state and negative partial transpose entangled states.