Oracle Separations for Quantum Statistical Zero-Knowledge

TL;DR

This paper explores the limitations of quantum statistical zero-knowledge proof systems by establishing oracle-based separations, demonstrating they cannot encompass certain complexity classes under relativized settings.

Contribution

It provides the first oracle separations showing quantum statistical zero-knowledge does not contain UP or coUP, advancing understanding of quantum proof system boundaries.

Findings

Quantum statistical zero-knowledge does not contain UP relative to some oracle.

Quantum statistical zero-knowledge does not contain UP relative to a random oracle.

The proofs use bounds on output state discrimination for relativized quantum circuits.

Abstract

This paper investigates the power of quantum statistical zero knowledge interactive proof systems in the relativized setting. We prove the existence of an oracle relative to which quantum statistical zero-knowledge does not contain UP intersect coUP, and we prove that quantum statistical zero knowledge does not contain UP relative to a random oracle with probability 1. Our proofs of these statements rely on a bound on output state discrimination for relativized quantum circuits based on the quantum adversary method of Ambainis, following a technique similar to one used by Ben-David and Kothari to prove limitations on a query complexity variant of quantum statistical zero-knowledge.