An efficient quantum parallel repetition theorem and applications
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916208657301504 |
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| author | Bostanci, John Qian, Luowen Spooner, Nicholas Yuen, Henry |
| author_facet | Bostanci, John Qian, Luowen Spooner, Nicholas Yuen, Henry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10681 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An efficient quantum parallel repetition theorem and applications Bostanci, John Qian, Luowen Spooner, Nicholas Yuen, Henry Quantum Physics Computational Complexity Cryptography and Security 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. |
| title | An efficient quantum parallel repetition theorem and applications |
| topic | Quantum Physics Computational Complexity Cryptography and Security |
| url | https://arxiv.org/abs/2311.10681 |