Construction of noisy bound entangled states and the range criterion

TL;DR

This paper develops methods to construct bipartite noisy bound entangled states with positive partial transpose that satisfy or violate the range criterion, using various product bases, advancing understanding of entanglement properties.

Contribution

It introduces schemes for constructing classes of noisy bound entangled states satisfying the range criterion and identifies states that do not, expanding the classification of entangled states.

Findings

Constructed distinct classes of noisy bound entangled states.

Identified states that do not satisfy the range criterion.

Explored different types of product bases for state construction.

Abstract

In this work we consider bipartite noisy bound entangled states with positive partial transpose, that is, such a state can be written as a convex combination of an edge state and a separable state. In particular, we present schemes to construct distinct classes of noisy bound entangled states which satisfy the range criterion. As a consequence of the present study we also identify noisy bound entangled states which do not satisfy the range criterion. All of the present states are constituted by exploring different types of product bases.