Entanglement-assisted capacities of compound quantum channels

TL;DR

This paper derives single-letter formulas for the capacities of entanglement-assisted quantum communication over compound channels, considering various knowledge and feedback scenarios, using decoupling bounds and smooth entropies.

Contribution

It provides the first comprehensive analysis of entanglement-assisted capacities for compound quantum channels with different informational settings.

Findings

Single-letter capacity formulas derived for all scenarios.

Capacities depend on channel knowledge and feedback.

Methods based on one-shot decoupling bounds and smooth entropies.

Abstract

We study universal quantum codes for entanglement-assisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.