Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels
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.
Cite
@article{arxiv.1308.6503,
title = {Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels},
author = {Marco Tomamichel and Vincent Y. F. Tan},
journal= {arXiv preprint arXiv:1308.6503},
year = {2015}
}
Comments
v2: main results significantly generalized and improved; v3: extended to image-additive channels, change of title, journal version