发表机构
UCSB; UIUC; NTT Research（加州大学圣塔芭芭拉分校; 伊利诺伊大学厄巴纳-香槟分校; NTT研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入高效NP辅助阴影层析成像，证明许多现有PRS和PRU架构（包括为规避单向函数而设计的）实际蕴含单向函数存在或NP困难，为未来构建提供否定性指导。
AI 中文摘要
量子密码学中的一个关键挑战是在不使用（量子可计算的）单向函数的情况下构建量子单向性和伪随机性。到目前为止，这已被证明是一项困难的任务，仅有少数几个不直接基于单向函数构建的候选方案。即使在这些少数候选方案中，我们也缺乏分析技术来确定所提出的构造何时可能无意中产生单向函数。在这项工作中，我们引入了量子态的高效NP辅助阴影层析成像。我们证明了{\em 可计算的}纯态集合可以通过高效的NP辅助阴影层析成像来学习，其中如果给定状态的有效制备电路的描述，任何计算基项上的振幅和相位都可以经典高效计算，则称该状态是可计算的。我们还给出了新的算法，用于在给定对酉算子的多项式多次查询的情况下进行NP辅助的酉算子学习。在此基础上，我们表明许多现有的PRS和PRU架构，包括一些明确为了规避单向函数而引入的架构（例如，哈密顿相位态，Bostanci等人，TQC 2025），实际上确实意味着单向函数的存在或意味着\NP困难。我们希望这些否定结果将为未来从可能不属于复杂性类NP的假设构建PRS和PRU的研究提供信息。
英文摘要
A key challenge in quantum cryptography is to build quantum one-wayness and pseudorandomness without the use of (quantum computable) one-way functions. So far, this has turned out to be a difficult task, with only a few proposed candidates that are not directly built from one-way functions. Even within these few proposed candidates, we have lacked the techniques to analyze when proposed constructions may inadvertently yield one-way functions. In this work, we introduce efficient NP-aided shadow tomography of quantum states. We prove that collections of {\em computable} pure states can be learned via efficient NP-aided shadow tomography, where we say that a state is computable if the amplitude and phase on any computational basis term can be classically efficiently computed given the description of an efficient preparation circuit for the state. We also give new algorithms for NP-aided learning of unitaries given polynomially many queries to the unitary. By building on this, we show that many existing architectures for PRS and PRU, including some that were explicitly introduced for the purposes of avoiding one-way functions (e.g., Hamiltonian Phase States, Bostanci et. al., TQC 2025), actually do imply the existence of one-way functions or imply \(\NP\) hardness. We hope that these no-go results will inform future investigations into building PRS and PRUs from assumptions that are plausibly outside the complexity class NP.
