On converse bounds for classical communication over quantum channels

TL;DR

This paper introduces new bounds for classical communication over quantum channels, including computable meta-converses and the $$-information, providing tighter capacity bounds and finite resource analyses.

Contribution

It presents novel, efficiently computable meta-converses and the $$-information bound, extending converse bounds to both one-shot and asymptotic regimes.

Findings

Activated no-signalling codes achieve Matthews-Wehner bound

New meta-converse bounds are efficiently computable

The $$-information provides tighter capacity bounds for covariant channels

Abstract

We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical communication can be achieved by activated, no-signalling assisted codes, suitably generalizing a result for classical channels. Second, we derive a new efficiently computable meta-converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel. As applications, we provide a finite resource analysis of classical communication over quantum erasure channels, including the second-order and moderate deviation asymptotics. Third, we explore the asymptotic analogue of our new meta-converse, the $\Upsilon$-information of the channel. We show that its regularization is an upper bound on the classical capacity, which is generally tighter than the entanglement-assisted capacity and other known efficiently computable strong converse bounds. For covariant channels we show that the $\Upsilon$-information is a strong converse bound.