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：我们展示了一个无条件的经典预言机分离，区分了可使用量子证明验证的语言类（$\mathsf{QMA}$）与可使用经典证明验证的语言类（$\mathsf{QCMA}$）。与Bostanci、Haferkamp、Nirkhe和Zhandry（STOC 2026）近期的工作相比，我们的证明在概念和技术上更为简洁，并能轻松扩展到其他预言机分离。特别地，我们的技术首次实现了可使用量子建议判定的语言类（$\mathsf{BQP}/\mathsf{qpoly}$）与可使用经典建议判定的语言类（$\mathsf{BQP}/\mathsf{poly}$）之间的无条件经典预言机分离，改进了Aaronson和Kuperberg（CCC 2007）的量子预言机分离以及Li、Liu、Pelecanos和Yamakawa（ITCS 2024）的经典可访问经典预言机分离。我们的预言机基于Yamakawa和Zhandry（FOCS 2022）引入的码交集问题，并结合了具有极佳列表恢复性质的码。