Correlated entanglement distillation and the structure of the set of undistillable states

TL;DR

This paper investigates how correlations among input states affect entanglement distillation, revealing that distillability depends only on reductions and establishing a convex hull relation for undistillable states.

Contribution

It introduces a novel framework linking correlated undistillable states to standard ones and proves a new activation result for entanglement distillation.

Findings

Correlated undistillable states form the convex hull of standard undistillable states.

Distillability depends solely on reductions, not correlations.

Existence of states enabling distillation when combined with certain undistillable states.

Abstract

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically-distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: it is shown that for every entangled state and every positive integer k, there exists a copy-correlated k-undistillable state such that their tensor product is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a non-positive partial transpose is discussed.