Zero-Error List Decoding for Classical-Quantum Channels

TL;DR

This paper investigates the zero-error capacity of pure-state classical-quantum channels with list decoding, providing bounds and highlighting differences from classical settings.

Contribution

It introduces bounds for list decoding capacity in quantum channels and reveals unique divergence behaviors not seen in classical channels.

Findings

Achievability bound for list-size two established.

Converse bound valid for all fixed list sizes.

Divergence of sphere-packing bound may not be achievable by zero-error list codes.

Abstract

The aim of this work is to study the zero-error capacity of pure-state classical-quantum channels in the setting of list decoding. We provide an achievability bound for list-size two and a converse bound holding for every fixed list size. The two bounds coincide for channels whose pairwise absolute state overlaps form a positive semi-definite matrix. Finally, we discuss a remarkable peculiarity of the classical-quantum case: differently from the fully classical setting, the rate at which the sphere-packing bound diverges might not be achievable by zero-error list codes, even when we take the limit of fixed but arbitrarily large list size.