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DOI: 10.4230/LIPIcs.OPODIS.2024.34

Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries

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

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

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.

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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)

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@InProceedings{legall_et_al:LIPIcs.OPODIS.2024.34,
  author =	{Le Gall, Fran\c{c}ois and Nadler, Oran and Nishimura, Harumichi and Oshman, Rotem},
  title =	{{Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.34},
  URN =		{urn:nbn:de:0030-drops-225701},
  doi =		{10.4230/LIPIcs.OPODIS.2024.34},
  annote =	{Keywords: SMP model, multi-party communication, quantum distributed algorithms}
}

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Quantum Simultaneous Protocols Without Public Coins Using Modified Equality Queries

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