Better transmission with lower capacity: lossy compression over quantum channels

TL;DR

This paper reveals that, unlike classical channels, quantum channels can have lower capacity but still produce less distortion in lossy transmission, challenging traditional notions of channel usefulness.

Contribution

The study demonstrates that in quantum communication, lower capacity channels can outperform higher capacity ones in terms of distortion at fixed rates, contrary to classical expectations.

Findings

Lower capacity quantum channels can cause less distortion than higher capacity channels.

Quantum channels exhibit non-classical behavior in rate-distortion trade-offs.

The results challenge classical assumptions about channel capacity and performance.

Abstract

Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication in the classical regime. Lossy compression scenarios require the additional description provided by rate-distortion theory, which characterizes the trade-off between compression rate and the distortion of the compressed signal. Even in this context, the capacity characterizes the usefulness of a channel -- a channel with more capacity will always outperform a channel with less capacity. We show that this is no longer true when sending classical information over a quantum channel. In particular, we find a pair of quantum channels where the channel with the lower capacity causes less distortion than the higher capacity channel when both are used at a fixed rate.