QMA在量子随机预言机模型中的简洁论证
Succinct Arguments for QMA in the Quantum Random Oracle Model
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- EPFL（洛桑联邦理工学院）
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中文总结 AI 辅助
本文在量子随机预言机模型中首次构造了针对QMA的简洁论证，仅依赖无结构困难性，通过编译量子交互式预言机证明并引入提取向量承诺，证明理想哈希函数足以支持QMA的简洁验证。
中文摘要 AI 辅助
简洁论证是一种基本的密码学原语，用于以少量通信验证计算声明。在经典环境中，针对NP的简洁论证可以仅由无结构困难性（例如哈希函数）构造，通过承诺-打开范式编译针对NP的概率可检验证明（PCP）或交互式预言机证明（IOP）。相比之下，已知的针对QMA的简洁论证依赖于“结构化”密码学原语，或依赖于量子PCP猜想。我们在量子随机预言机模型（QROM）中构造了第一个针对QMA的简洁论证，无需依赖额外的密码学假设或未经证明的猜想。这从无结构困难性中产生了针对QMA的简洁论证，表明理想哈希函数不仅足以用于针对NP的简洁论证，也足以用于针对QMA的简洁论证。我们结果的基础是一种保持效率的变换，该变换通过自然的量子承诺-打开范式，将量子交互式预言机证明（QIOP）（一种最近引入的量子PCP的交互式推广）编译为针对同一语言的量子论证。我们的变换适用于每个具有公开查询可靠性（public-query soundness）的QIOP，我们形式化了这一概念以捕捉承诺-打开范式的自然要求，并且已知的针对QMA的QIOP满足这一要求。作为我们变换中的一个关键成分，我们在QROM中形式化并构造了针对量子状态的具有局部打开的提取向量承诺，这可能具有独立的意义。
英文摘要
Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
