An efficient quantum parallel repetition theorem and applications

Fuente: arXiv
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Main Authors: Bostanci, John, Qian, Luowen, Spooner, Nicholas, Yuen, Henry
Format: Preprint
Published: 2023
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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