Oracle Separations Between Quantum and Non-interactive Zero-Knowledge Classes

Abstract: We study the relationship between problems solvable by quantum algorithms in polynomial time and those for which zero-knowledge proofs exist. In prior work, Aaronson [arxiv:quant-ph/0111102] showed an oracle separation between BQP and SZK, i.e. an oracle $A$ such that $\mathrm{SZK}^A \not\subseteq \mathrm{BQP}^A$. In this paper we give a simple extension of Aaronson's result to non-interactive zero-knowledge proofs with perfect security. This class, NIPZK, is the most restrictive zero-knowledge class. We show that even for this class we can construct an $A$ with $\mathrm{NIPZK}^A \not\subseteq \mathrm{BQP}^A$.