发表机构
Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造经典神谕分离QMA与QCIP，证明某些问题确实需要量子证明，并加强QMA-QCMA分离，技术上将密码学方法引入复杂性理论。
AI 中文摘要
某些问题是否需要量子证明一直是量子复杂性理论中的一个核心问题（Aharonov和Naveh，2002；Aaronson和Kuperberg，CCC 2007）。最近，Bostanci、Haferkamp、Nirkhe和Zhandry（STOC 2026）的突破性工作，以及随后Bostanci、Huang和Vaikuntanathan（FOCS 2026）给出的更简单的分离，建立了QMA与QCMA之间的经典神谕分离。然而，尽管这两个分离中使用的问题不在QCMA中，它们仍然属于AM：它们具有带经典验证者的两消息公开硬币证明系统。在本工作中，我们询问某些问题是否真正需要量子证明。更正式地，我们考虑由Buhrman、Le Gall和Weggemans（2024）引入的复杂性类QCIP，其中高效的量子验证者通过经典信道与无界证明者进行任意多项式轮数的交互。我们构造了一个经典神谕O，使得QMA^O不包含于QCIP^O，从而表明某些语言确实需要量子证明，且没有经典替代方案。由于QCMA=QCIP[1]，这加强了早期的QMA-QCMA分离，现在这些分离作为我们结果的特例而成立。作为技术贡献，我们将Cakan、Goyal和Shmueli（CRYPTO 2026）在密码学背景下为分析经典交互量子机器而开发的技术扩展到复杂性理论环境中。我们相信这可能具有独立的意义。
英文摘要
Whether some problems require quantum proofs has been a central question in quantum complexity (Aharonov and Naveh, 2002; Aaronson and Kuperberg, CCC 2007). Recently, breakthrough work of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC 2026), followed by a simpler separation due to Bostanci, Huang, and Vaikuntanathan (FOCS 2026), established a classical oracle separation between $\mathsf{QMA}$ and $\mathsf{QCMA}$. However, while they are not in $\mathsf{QCMA}$, the problems used in both separations still lie in $\mathsf{AM}$: they admit a two-message public-coin proof system with a classical verifier. In this work, we ask whether some problems truly require quantum proofs. More formally, we consider the complexity class $\mathsf{QCIP}$, introduced by Buhrman, Le Gall, and Weggemans (2024), where an efficient quantum verifier interacts with an unbounded prover over a classical channel for an arbitrary polynomial number of rounds. We construct a classical oracle $\mathcal{O}$ such that $\mathsf{QMA}^{\mathcal{O}}\not\subseteq\mathsf{QCIP}^{\mathcal{O}}$, thus showing that some languages indeed require quantum proofs, with no classical replacements. Since $\mathsf{QCMA}=\mathsf{QCIP}[1]$, this strengthens the earlier $\mathsf{QMA}$--$\mathsf{QCMA}$ separations, which now follow as a special case of our result. As a technical contribution, we extend to the complexity theory setting the techniques developed by Cakan, Goyal, and Shmueli (CRYPTO 2026) in the context of cryptography for analyzing classically interacting quantum machines. We believe this may be of independent interest.
