The apex of the family tree of protocols: Optimal rates and resource inequalities

TL;DR

This paper establishes optimal bounds on entanglement gain and quantum communication cost for the Fully Quantum Slepian-Wolf protocol in the one-shot regime, connecting these to asymptotic rates and resource inequalities.

Contribution

It introduces a resource inequality for the one-shot FQSW protocol and derives bounds on one-shot quantum capacity and state redistribution rates.

Findings

Bounds on entanglement gain and quantum communication cost in one-shot regime

Explicit proof of asymptotic rate optimality

Resource inequality for one-shot FQSW protocol

Abstract

We establish bounds on the maximum entanglement gain and minimum quantum communication cost of the Fully Quantum Slepian-Wolf protocol in the one-shot regime, which is considered to be at the apex of the existing family tree in Quantum Information Theory. These quantities, which are expressed in terms of smooth min- and max-entropies, reduce to the known rates of quantum communication cost and entanglement gain in the asymptotic i.i.d. scenario. We also provide an explicit proof of the optimality of these asymptotic rates. We introduce a resource inequality for the one-shot FQSW protocol, which in conjunction with our results, yields achievable one-shot rates of its children protocols. In particular, it yields bounds on the one-shot quantum capacity of a noisy channel in terms of a single entropic quantity, unlike previously bounds. We also obtain an explicit expression for the achievable rate for one-shot state redistribution.