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：本研究旨在探讨列表译码设定下纯态经典-量子信道的零错误容量。我们针对列表尺寸为2的情形给出了可达性界，并针对任意固定列表尺寸给出了逆界。当信道成对绝对态重叠构成半正定矩阵时，这两个界相互吻合。最后，我们讨论了经典-量子情形的一个显著特性：与完全经典设定不同，即使考虑固定但任意大的列表尺寸极限，球堆积界发散所对应的速率也可能无法通过零错误列表码实现。