It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly $\neq$ BQP/poly or QMA $\neq$ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly $\neq$ BQP/poly and QMA $\neq$ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.

翻译：长久以来，构建一个经典谕示使得BQP/qpoly ≠ BQP/poly 或 QMA ≠ QCMA 是一个悬而未决的问题。本文中，我们构造了经典可访问的经典谕示，使得在这些谕示下BQP/qpoly ≠ BQP/poly 且 QMA ≠ QCMA。这里，经典可访问的经典谕示是指即使对量子算法也只能通过经典方式访问的谕示。基于类似的技术，我们还展示了在分布性量子可访问经典谕示下QMA和QCMA分离的另一种证明，该分离结果近期由Natarajan和Nirkhe给出。