One-shot entanglement-assisted quantum and classical communication

TL;DR

This paper characterizes one-shot entanglement-assisted quantum and classical communication capacities over quantum channels, providing bounds that unify finite and asymptotic scenarios through smoothed entropic quantities.

Contribution

It introduces bounds on one-shot capacities using smoothed entropies, bridging finite and asymptotic cases, and generalizes mutual information to the one-shot setting.

Findings

Bounds converge to known formulas for memoryless channels in the asymptotic limit

One-shot capacities characterized by the difference of two smoothed entropic quantities

The difference acts as a one-shot analogue of mutual information

Abstract

We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain characterizations of the corresponding one-shot capacities by establishing upper and lower bounds on them in terms of the difference of two smoothed entropic quantities. In the case of a memoryless channel, the upper and lower bounds converge to the known single-letter formulas for the corresponding capacities, in the limit of asymptotically many uses of it. Our results imply that the difference of two smoothed entropic quantities characterizing the one-shot entanglement-assisted capacities serves as a one-shot analogue of the mutual information, since it reduces to the mutual information, between the output of the channel and a system purifying its input, in the asymptotic, memoryless scenario.