Construction of Bound Entangled States Based on Permutation Operators

TL;DR

This paper introduces a method to generate new bound entangled states in bipartite systems using permutation operators, ensuring they are PPT and violate the range criterion, thus expanding the class of known bound entangled states.

Contribution

The paper presents a novel construction technique for bound entangled states based on permutation operators, applicable to arbitrary dimensions, and demonstrates their distinctness from original states.

Findings

Constructed new bound entangled states using permutation operators.

Proved the new states are PPT and violate the range criterion.

Showed the new states are not local unitary equivalent to original states.

Abstract

We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial transpose) and violate the range criterion at the same time. By applying certain operators to given bound entangled states or to one of the subsystems of the given bound entangled states, we obtain a set of new states which are both PPT and violate the range criterion. We show that the derived bound entangled states are not local unitary equivalent to the original bound entangled states by detail examples.