发表机构
Carnegie Mellon University; Academia Sinica; California Institute of Technology（卡内基梅隆大学; 中央研究院; 加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构造经典预言机，证明可克隆量子证明仍比经典证明更强大，解决了开放问题，并应用于量子密码学。
AI 中文摘要
自从复杂性类 QMA 作为 NP 的量子验证者类比被引入以来（Kitaev，1997），许多人一直想知道量子证明是否是必要的，或者经典证明是否就足够了——也就是说，QMA 是否等于 QCMA，或者 QCMA 是否不等于 QMA（Aharonov 和 Naveh，2002；Aaronson 和 Kuperberg，CCC '07）。这个长期存在的问题最近被 Bostanci、Haferkamp、Nirkhe 和 Zhandry（STOC '26）以及 Bostanci、Huang 和 Vaikuntanathan（FOCS '26）的工作所回答，他们表明在经典预言机设置中，量子证明比经典证明更强大。然而，目前仍不清楚究竟是什么使得量子证明比经典证明更强大。在信息论设置中，一族量子态不可经典化当且仅当它是不可克隆的。事实上，这些近期工作也明确强调其量子证明的不可克隆性是其分离背后的关键机制，并且他们的论证关键性地依赖于这一性质。这引发了一个问题：不可克隆性是否是量子证明比经典证明更强大的必要条件。在这项工作中，我们通过构造一个经典预言机 O 使得 QCMA^O != ClonableQMA^O，表明即使是可克隆的量子证明相对于经典预言机也可以比经典证明更强大。这解决了 Nehoran 和 Zhandry（ITCS '24）的开放问题，他们建立了相对于量子预言机的类似分离。我们还展示了 BQP/clonableqpoly 和 BQP/poly 之间的经典预言机分离，并将我们的结果应用于量子密码学。
英文摘要
Since the introduction of the complexity class QMA as a quantum-verifier analogue of NP (Kitaev, 1997), many have wondered whether quantum proofs are necessary or classical proofs suffice - that is, whether QMA = QCMA or QCMA != QMA (Aharonov and Naveh, 2002; Aaronson and Kuperberg, CCC '07). This longstanding question was recently answered by works of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC '26) and Bostanci, Huang, and Vaikuntanathan (FOCS '26), which showed that quantum proofs are more powerful than classical ones in the classical-oracle setting. However, it remains unclear what exactly makes quantum proofs more powerful than classical ones. In the information-theoretic setting, a family of quantum states is not classicalizable if and only if it is unclonable. Indeed, these recent works also explicitly highlight the unclonability of their quantum proofs as a key mechanism behind their separations, and their arguments crucially rely on this property. This raises the question of whether unclonability is necessary for quantum proofs to be more powerful than classical ones. In this work, we show that even clonable quantum proofs can be more powerful than classical ones relative to a classical oracle by constructing a classical oracle O such that QCMA^O != ClonableQMA^O. This resolves the open question of Nehoran and Zhandry (ITCS '24), who established the analogous separation relative to a quantum oracle. We also show a classical-oracle separation between BQP/clonableqpoly and BQP/poly, and give applications of our results to quantum cryptography.
