New Partial Trace Inequalities and Distillability of Werner States

TL;DR

This paper introduces new partial trace inequalities and applies them to analyze the distillability of Werner states, offering a dimension-independent bound and connecting inequalities with state separability.

Contribution

It develops a novel approach translating Werner state distillability into partial trace inequalities and presents new inequalities applicable to various matrix families.

Findings

New bound for 2-distillability of Werner states independent of system dimension

Established new partial trace inequalities related to bipartite system separability

Connected partial trace inequalities with Werner state properties

Abstract

One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable. This problem has been open for almost 30 years, and still no one has been able to give a complete answer to it. This work presents a new strategy to try to solve this problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities, this is the aim of our first main result. As a consequence we obtain a new bound for the $2$-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states. Throughout this work we also present numerous partial trace inequalities, which are valid for many families of matrices.