Entanglement Witnesses and Characterizing Entanglement Properties of Some PPT States

TL;DR

This paper develops new entanglement witnesses for 3x3 and 4x4 quantum systems using linear programming, enabling the detection of entanglement in PPT states through an infinite family of non-decomposable witnesses.

Contribution

It introduces a novel linear programming approach to construct infinite families of non-decomposable entanglement witnesses for higher-dimensional systems.

Findings

Constructed EWs contact feasible regions without intersecting them.

Created an infinite set of EWs by rotating hyper-planes around contact areas.

EWs successfully detect entanglement in some PPT states.

Abstract

On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3x3 and 4x4 systems are constructed. In both cases, the constructed EWs correspond to the hyperplanes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).