Commitment capacity of classical-quantum channels

TL;DR

This paper investigates the capacity of classical-quantum channels for commitment schemes, establishing bounds based on conditional entropy and extending classical techniques to the quantum setting with new constructions.

Contribution

It defines commitment capacity for classical-quantum channels and proves matching bounds, extending classical methods with novel quantum constructions.

Findings

Established upper and lower bounds on commitment capacity

Extended classical techniques to quantum channels

Introduced new constructions for quantum commitment bounds

Abstract

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.