We show an unconditional classical oracle separation between the class of languages that can be verified using a quantum proof ($\mathsf{QMA}$) and the class of languages that can be verified with a classical proof ($\mathsf{QCMA}$). Compared to the recent work of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC 2026), our proof is conceptually and technically simpler, and readily extends to other oracle separations. In particular, our techniques yield the first unconditional classical oracle separation between the class of languages that can be decided with quantum advice ($\mathsf{BQP}/\mathsf{qpoly}$) and the class of languages that can be decided with classical advice ($\mathsf{BQP}/\mathsf{poly}$), improving on the quantum oracle separation of Aaronson and Kuperberg (CCC 2007) and the classically-accessible classical oracle separation of Li, Liu, Pelecanos and Yamakawa (ITCS 2024). Our oracles are based on the code intersection problem introduced by Yamakawa and Zhandry (FOCS 2022), combined with codes that have extremely good list-recovery properties.

翻译：我们展示了在量子证明（$\mathsf{QMA}$）可验证语言类与经典证明（$\mathsf{QCMA}$）可验证语言类之间无条件的经典谕示分离。与Bostanci、Haferkamp、Nirkhe和Zhandry（STOC 2026）的近期工作相比，我们的证明在概念和技术上更为简洁，并可轻易推广至其他谕示分离。特别地，我们的技术首次实现了量子建议可判定语言类（$\mathsf{BQP}/\mathsf{qpoly}$）与经典建议可判定语言类（$\mathsf{BQP}/\mathsf{poly}$）之间无条件的经典谕示分离，改进了Aaronson与Kuperberg（CCC 2007）的量子谕示分离以及Li、Liu、Pelecanos与Yamakawa（ITCS 2024）的经典可访问经典谕示分离。我们的谕示基于Yamakawa与Zhandry（FOCS 2022）提出的码交问题，并结合了具有极优列表恢复特性的码。