On two-distillable Werner states

TL;DR

This paper investigates the distillability properties of Werner states in bipartite quantum systems, providing evidence for a conjecture that certain NPT Werner states are not two-distillable, which has implications for quantum entanglement theory.

Contribution

The paper offers new formulations and evidence supporting the conjecture that some Werner states are not two-distillable, advancing understanding of quantum entanglement.

Findings

Evidence supporting the conjecture that certain Werner states are not two-distillable

Multiple formulations of the problem are provided

Clarification of the classification of Werner states based on distillability

Abstract

We consider bipartite mixed states in a $d\otimes d$ quantum system. We say that $\rho$ is PPT if its partial transpose $1 \otimes T (\rho)$ is positive semidefinite, and otherwise $\rho$ is NPT. The well-known Werner states are divided into three types: (a) the separable states (the same as the PPT states); (b) the one-distillable states (necessarily NPT); and (c) the NPT states which are not one-distillable. We give several different formulations and provide further evidence for validity of the conjecture that the Werner states of type (c) are not two-distillable.