Distilling entanglement from arbitrary resources

TL;DR

This paper derives a general formula for the optimal rate of singlet distillation from any entangled resource using LOCC, extending previous results to arbitrary, non-i.i.d. resources with a quantum information spectrum approach.

Contribution

It introduces a universal formula for entanglement distillation rates applicable to arbitrary resources, generalizing prior i.i.d.-based formulas with a new one-shot hashing bound.

Findings

Derived a general formula for entanglement distillation rate

Extended the hashing bound to one-shot scenarios

Unified the distillation theory for arbitrary resources

Abstract

We obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource, by means of local operations and classical communication (LOCC). Our formula, obtained by employing the quantum information spectrum method, reduces to that derived by Devetak and Winter, in the special case of an i.i.d. resource. The proofs rely on a one-shot version of the so-called "hashing bound," which in turn provides bounds on the one-shot distillable entanglement under general LOCC.