Extremal extensions of entanglement witnesses: Unearthing new bound entangled states

TL;DR

This paper develops extremal extensions of entanglement witnesses derived from Choi's map to detect and uncover new bound entangled states, enhancing the understanding of PPT entanglement.

Contribution

It introduces a generalized construction of extremal entanglement witnesses based on Osaka's extension of Choi's map, enabling detection of previously unrecognized PPT entangled states.

Findings

Successfully detected new PPT entangled states

Constructed entangled states using Cholesky-like decomposition

Enhanced entanglement detection capabilities

Abstract

In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map due to Osaka, from which we construct entanglement witnesses. These extremal extensions are powerful in terms of their capacity to detect entanglement of positive under partial transpose (PPT) entangled states and lead to unearthing of entanglement of new PPT states. We also use the Cholesky-like decomposition to construct entangled states which are revealed by these extremal entanglement witnesses.