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