  Bit commitment schemes are at the basis of modern cryptography. Since
information-theoretic security is impossible both in the classical and the
quantum regime, we need to look at computationally secure commitment schemes.
In this paper, we study worst-case complexity assumptions that imply quantum
bit-commitment schemes. First, we show that QSZK not included in QMA implies a
computationally hiding and statistically binding auxiliary-input quantum
commitment scheme. Additionally, we give auxiliary-input commitment schemes
using quantum advice that depend on the much weaker assumption that QIP is not
included in QMA (which is weaker than PSPACE not included in PP). Finally, we
find a quantum oracle relative to which honest-verifier QSZK is not contained
in QCMA, the class of languages that can be verified using a classical proof in
quantum polynomial time.

Quantum Physics