Resource Cost Results for Entanglement Distillation and State Merging under Source Uncertainties

TL;DR

This paper develops one-way LOCC protocols for quantum state merging and entanglement distillation under source uncertainties, achieving optimal resource costs and highlighting limitations of classical robustification methods.

Contribution

It introduces new protocols for compound sources and determines capacities for AVQS, revealing that classical robustification can be suboptimal in quantum state merging.

Findings

Protocols achieve asymptotically optimal resource costs

Determination of one-way entanglement distillation capacity for AVQS

Robustification may lead to suboptimal costs in quantum state merging

Abstract

We introduce one-way LOCC protocols for quantum state merging for compound sources, which have asymptotically optimal entanglement as well as classical communication resource costs. For the arbitrarily varying quantum source (AVQS) model, we determine the one-way entanglement distillation capacity, where we utilize the robustification and elimination techniques, well-known from classical as well as quantum channel coding under assumption of arbitrarily varying noise. Investigating quantum state merging for AVQS, we demonstrate by example, that the usual robustification procedure leads to suboptimal resource costs in this case.