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Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries

Authors François Le Gall , Oran Nadler, Harumichi Nishimura, Rotem Oshman

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Author Details

François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan
Oran Nadler
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Japan
Rotem Oshman
  • Blavatnik School of Computer Science, Tel Aviv University, Israel

Funding

  • Le Gall, François: JSPS KAKENHI grants Nos. JP20H05966, 20H00579, 24H00071, MEXT Q-LEAP grant No. JPMXS0120319794 and JST CREST grant No. JPMJCR24I4.
  • Nishimura, Harumichi: JSPS KAKENHI grants Nos. JP20H05966, 22H00522, 24H00071, 24K22293, MEXT Q-LEAP grant No. JPMXS0120319794 and JST CREST grant No. JPMJCR24I4.
  • Oshman, Rotem: ISF grants Nos. 2801/20 and 3725/24 and NSF-BSF grant No. 2022699.

Cite As Get BibTex

François Le Gall, Oran Nadler, Harumichi Nishimura, and Rotem Oshman. Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.34

Abstract

In this paper we study a quantum version of the multiparty simultaneous message-passing (SMP) model, and we show that in some cases, quantum communication can replace public randomness, even with no entanglement between the parties. This was already known for two players, but not for more than two players, and indeed, so far all that was known was a negative result. Our main technical contribution is a compiler that takes any classical public-coin simultaneous protocol based on "modified equality queries," and converts it into a quantum simultaneous protocol without public coins with roughly the same communication complexity. We then use our compiler to derive protocols for several problems, including frequency moments, neighborhood diversity, enumeration of isolated cliques, and more.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum communication complexity
Keywords
  • SMP model
  • multi-party communication
  • quantum distributed algorithms

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