Quantum Commitments from Complexity Assumptions

We study worst-case complexity assumptions that imply quantum bit-commitment schemes. First we show that QSZK \(\not\subseteq\) QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. We then extend our result to show that the much weaker assumption QIP \(\not\subseteq\) QMA (which is weaker than PSPACE \(\not\subseteq\) PP) implies the existence of auxiliary-input commitment schemes with quantum advice. Finally, to strengthen the plausibility of the separation QSZK \(\not\subseteq\) QMA we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA.