One-shot rates for entanglement manipulation under non-entangling maps

TL;DR

This paper derives the optimal rates for one-shot entanglement manipulation under nearly non-entangling operations, linking these rates to various entanglement measures and exploring their asymptotic behavior.

Contribution

It provides explicit formulas for one-shot entanglement manipulation rates and connects them to established entanglement measures, offering new operational insights.

Findings

Optimal rates expressed via max- and min-relative entropies

Operational meaning assigned to robustness measures

Partial recovery of entanglement reversibility in the asymptotic limit

Abstract

We obtain expressions for the optimal rates of one- shot entanglement manipulation under operations which generate a negligible amount of entanglement. As the optimal rates for entanglement distillation and dilution in this paradigm, we obtain the max- and min-relative entropies of entanglement, the two logarithmic robustnesses of entanglement, and smoothed versions thereof. This gives a new operational meaning to these entanglement measures. Moreover, by considering the limit of many identical copies of the shared entangled state, we partially recover the recently found reversibility of entanglement manipu- lation under the class of operations which asymptotically do not generate entanglement.