Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any $T$-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.

翻译：简洁论证系统在现代密码学中具有核心重要性，能够高效验证计算主张。在经典设定中，Kilian (STOC 92) 证明，任何针对NP的概率可检验证明均可仅通过抗碰撞哈希函数转化为针对NP的简洁论证系统。而在量子设定中，近期工作已确立面向QMA（需*量子*证明的命题）的（经典可验证）简洁论证的可行性。然而，所有已知构造均依赖于高度结构化的"带误差学习"（LWE）假设，这与足以支撑NP的非结构化假设形成鲜明对比。本文提出一种新框架，拓展了面向QMA的简洁论证的密码学基础。我们假设存在：(i) 不经意态制备协议（OSP），该协议可基于*朴素*陷门无爪函数构造；(ii) 坍缩哈希函数——抗碰撞性的量子类比。特别地，我们首次获得了不依赖LWE困难性的面向QMA的简洁、经典可验证论证系统。构造分两步进行：首先，仅基于OSP假设设计一个*轮高效*的经典可验证论证系统；其次，引入一个*广义通信压缩编译器*，该编译器在假设存在坍缩哈希函数的前提下，可将任意$T$-轮交互协议转化为通信规模受限于$T \cdot \poly(\secp)$（其中$\poly$为独立于原始消息大小的固定多项式）的协议。我们的编译器扩展了Zhang (QCrypt 25) 基于量子刚性的通信压缩技术，并可能具有独立的研究价值。