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.

翻译：本工作旨在研究纯态经典量子信道在列表译码设置下的零误差容量。我们给出了列表大小为二时的可达界，以及一个适用于任意固定列表大小的逆界。对于其成对态绝对交叠构成半正定矩阵的信道，这两个界是重合的。最后，我们讨论了经典量子情形的一个显著特性：与完全经典情形不同，球面填充界发散所对应的速率可能无法通过零误差列表码实现，即使我们考虑固定但任意大的列表尺寸极限。