We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled to an equivalent $3$-message argument system, mirroring the transformation for quantum proof systems [KW00, KKMV07]. As immediate applications, we show how to derive hardness amplification theorems for quantum bit commitment schemes (answering a question of Yan [Yan22]), EFI pairs (answering a question of Brakerski, Canetti, and Qian [BCQ23]), public-key quantum money schemes (answering a question of Aaronson and Christiano [AC13]), and quantum zero-knowledge argument systems. We also derive an XOR lemma [Yao82] for quantum predicates as a corollary.

翻译：我们证明了一个针对高效挑战者与高效敌手之间3条消息的计算安全量子交互协议的紧致并行重复定理。同时，在合理假设下，我们证明了4条消息的计算安全协议的安全性通常不会因并行重复而降低。这些结果与Bellare、Impagliazzo和Naor的经典结果[BIN97]相呼应。最后，我们证明所有量子论证系统均可通过通用编译转化为等价的3条消息论证系统，这与量子证明系统的变换方式[KW00, KKMV07]一致。作为直接应用，我们展示了如何推导量子比特承诺方案（回答了Yan[Yan22]的问题）、EFI对（回答了Brakerski、Canetti和Qian[BCQ23]的问题）、公钥量子货币方案（回答了Aaronson和Christiano[AC13]的问题）以及量子零知识论证系统的硬度放大定理。此外，我们还将Yao的XOR引理[Yao82]推广至量子谓词情形作为推论。