Zero-Error List Decoding for Classical-Quantum Channels
For quantum information theorists, this work identifies a fundamental difference between classical and classical-quantum zero-error list decoding.
This paper studies zero-error capacity of pure-state classical-quantum channels under list decoding, providing achievability and converse bounds that coincide for channels with positive semi-definite overlap matrices. It reveals that, unlike classical channels, the sphere-packing bound divergence rate may not be achievable even with arbitrarily large list sizes.
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.