Entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels

TL;DR

This paper establishes single-letter formulas for the entanglement-assisted classical capacities of compound and arbitrarily varying quantum channels, revealing differences in the strong converse property between the two models.

Contribution

It provides the first single-letter characterizations of capacities for these quantum channel models and analyzes the strong converse property in detail.

Findings

Single-letter capacity formulas derived for both channel types.

Entanglement-assisted capacity lacks strong converse for some compound channels.

Strong converse holds for all arbitrarily varying quantum channels.

Abstract

We consider classical message transmission under entanglement assistance for compound memoryless and arbitrarily varying quantum channels. In both cases, we prove general coding theorems together with corresponding weak converse bounds. In this way, we obtain single-letter characterizations of the entanglement-assisted classical capacities for both channel models. Moreover, we show that the entanglement-assisted classical capacity does exhibit no strong converse property for some compound quantum channels for the average as well as the maximal error criterion. A strong converse to the entanglement-assisted classical capacities does hold for each arbitrarily varying quantum channel.