Constructing Entanglement Witness Via Real Skew-Symmetric Operators

TL;DR

This paper introduces a new class of entanglement witnesses constructed using real skew-symmetric operators, extending their applicability to various bipartite systems and analyzing their effectiveness in detecting PPT entangled states.

Contribution

It proposes a canonical form for these witnesses, extends the method to different system dimensions, and studies their optimality and entanglement detection capabilities.

Findings

Existence of multiple EWs for given bipartite dimensions

Detection of PPT entangled states by constructed witnesses

Extension of canonical EWs to enhance detection power

Abstract

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.