Commitment capacity of classical-quantum channels

We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of capacity these channels and prove matching upper lower bound on it in terms the conditional entropy. Our achievability (lower bound) proof is quantum generalisation work one authors (arXiv:2103.11548) which studied problem secure list decoding its application to bit-string commitment. The techniques use converse (upper similar spirit introduced by Winter, Nascimento Imai (Cryptography Coding 2003) classical However, technique case not so straightforward requires some new constructions, can be independent interest.