  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.
