Generalized relative entropies and the capacity of classical-quantum channels

TL;DR

This paper establishes bounds on the capacity of classical-quantum channels using generalized relative entropies, specifically Hoeffding and max-relative entropies, providing new insights into quantum information transmission limits.

Contribution

It introduces bounds on channel capacity based on Hoeffding and max-relative entropies, extending the theoretical framework for quantum communication analysis.

Findings

Lower bound expressed via Hoeffding capacity

Upper bound based on max-relative entropy divergence radius

Provides a theoretical framework for quantum channel capacity limits

Abstract

We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeffding capacity, that we define similarly to the Holevo capacity, but replacing the relative entropy with the Hoeffding distance. Similarly, our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max-relative entropy in the definition of the divergence radius of a channel.