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

Understand

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.