In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof techniques that do not relativize with respect to quantum oracles will also not relativize with respect to classical oracles. In this note, we show that this is not the case: specifically, we show that there is a quantum oracle problem that is contained in the class QMA, but not in a class we call polyQCPH. The class polyQCPH is equal to PSPACE with respect to classical oracles, and it is a well-known result that QMA is contained in PSPACE (also with respect to classical oracles). We also show that the same separation holds relative to a distributional oracle, which is a model introduced by Natarajan and Nirkhe (2024). We believe our findings show the need for some caution when using these non-standard oracle models, particularly when showing separations between quantum and classical resources.

翻译：近年来，Aaronson和Kuperberg（2007）提出的量子预言机模型在展示复杂性类与密码学原语之间的预言机分离方面得到了广泛应用。学界普遍认为，对于量子预言机不可相对化的证明技术，对于经典预言机同样不可相对化。本文指出，这一假设并不成立：具体而言，我们证明存在一个量子预言机问题包含于QMA类，但不包含于我们称为polyQCPH的类中。相对于经典预言机，polyQCPH类等价于PSPACE，而众所周知QMA包含于PSPACE（同样相对于经典预言机）。我们还证明，在Natarajan和Nirkhe（2024）提出的分布预言机模型中，该分离关系同样成立。我们认为，这些发现表明在使用这些非标准预言机模型时需要保持谨慎，特别是在展示量子与经典资源之间的分离关系时。