Brief Announcement: Distributed Quantum Proofs for Replicated Data

Authors Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, Ami Paz

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Author Details

Pierre Fraigniaud
  • IRIF, CNRS and Université de Paris, France
François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Japan
Ami Paz
  • Faculty of Computer Science, Universität Wien, Austria

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Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, and Ami Paz. Brief Announcement: Distributed Quantum Proofs for Replicated Data. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


This paper tackles the issue of checking that all copies of a large data set replicated at several nodes of a network are identical. The fact that the replicas may be located at distant nodes prevents the system from verifying their equality locally, i.e., by having each node consult only nodes in its vicinity. On the other hand, it remains possible to assign certificates to the nodes, so that verifying the consistency of the replicas can be achieved locally. However, we show that, as the replicated data is large, classical certification mechanisms, including distributed Merlin-Arthur protocols, cannot guarantee good completeness and soundness simultaneously, unless they use very large certificates. The main result of this paper is a distributed quantum Merlin-Arthur protocol enabling the nodes to collectively check the consistency of the replicas, based on small certificates, and in a single round of message exchange between neighbors, with short messages. In particular, the certificate-size is logarithmic in the size of the data set, which gives an exponential advantage over classical certification mechanisms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum communication complexity
  • Theory of computation → Distributed computing models
  • Quantum Computing
  • Distributed Network Computing
  • Algorithmic Aspects of Networks


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  1. Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, and Ami Paz. Distributed quantum proofs for replicated data. arXiv:2002.10018, 2020. URL:
  2. Pierre Fraigniaud, Boaz Patt-Shamir, and Mor Perry. Randomized proof-labeling schemes. Distributed Computing, 32(3):217-234, 2019. URL:
  3. Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12:19:1-19:33, 2016. URL:
  4. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. URL: