Brief Announcement: Distributed Quantum Interactive Proofs
The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs.
In this brief announcement, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The main result of this paper shows that by using quantum distributed interactive proofs, the number of interactions can be significantly reduced. More precisely, our main result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to 3-turn. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well.
distributed interactive proofs
distributed verification
quantum computation
Theory of computation~Distributed algorithms
Theory of computation~Quantum computation theory
48:1-48:3
Brief Announcement
FLG was supported by the JSPS KAKENHI grants JP16H01705, JP19H04066, JP20H00579, JP20H04139, JP20H05966, JP21H04879 and by the MEXT Q-LEAP grants JPMXS0118067394 and JPMXS0120319794. MM was supported by JST, the establishment of University fellowships towards the creation of science technology innovation, Grant Number JPMJFS2120. HN was supported by the JSPS KAKENHI grants JP19H04066, JP20H05966, JP21H04879, JP22H00522 and by the MEXT Q-LEAP grants JPMXS0120319794.
https://arxiv.org/abs/2210.01390
François
Le Gall
François Le Gall
Graduate School of Mathematics, Nagoya University, Japan
Masayuki
Miyamoto
Masayuki Miyamoto
Graduate School of Mathematics, Nagoya University, Japan
Harumichi
Nishimura
Harumichi Nishimura
Graduate School of Informatics, Nagoya University, Japan
10.4230/LIPIcs.DISC.2022.48
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François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura
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