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arXiv · 2311.10681

An efficient quantum parallel repetition theorem and applications

John Bostanci·Luowen Qian·Nicholas Spooner·Henry Yuen
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Abstract

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.

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John Bostanci, Luowen Qian, Nicholas Spooner, Henry Yuen. 2023-11-17. An efficient quantum parallel repetition theorem and applications. https://doi.org/10.1145/3618260.3649603

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