用优良码分离量子和经典建议
Separating Quantum and Classical Advice with Good Codes
AI总结：
本文通过构造优良码，实现了量子证明验证（QMA）与经典证明验证（QCMA）之间的无条件经典 oracle 分离，并扩展到其他 oracle 分离问题。
摘要：
我们展示了量子证明验证（QMA）所接受的语言类与经典证明验证（QCMA）所接受的语言类之间的无条件经典 oracle 分离。与 Bostanci 等人的最近工作相比，我们的证明在概念和技术上更简单，并可扩展到其他 oracle 分离。特别地，我们的技术提供了首次无条件经典 oracle 分离，将量子建议决定（BQP/qpoly）与经典建议决定（BQP/poly）的语言类分开，改进了 Aaronson 和 Kuperberg（CCC 2007）的量子 oracle 分离以及 Li 等人（ITCS 2024）的经典可访问经典 oracle 分离。我们的 oracle 基于 Yamakawa 和 Zhandry（FOCS 2022）引入的码交集问题，结合具有极佳列表恢复性质的码。
英文摘要：
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.
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