Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

TL;DR

This paper analyzes the finite-blocklength limits of transmitting classical information over image-additive quantum channels, revealing a second-order approximation governed by a new channel parameter called dispersion.

Contribution

It introduces a second-order approximation for the classical capacity of image-additive quantum channels, including a novel channel dispersion parameter with a geometric interpretation.

Findings

Second-order capacity approximation for quantum channels.

Introduction of the channel dispersion parameter.

Convergence rate of coding rate to Holevo capacity.

Abstract

We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. We consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.