Quantum Simultaneous Protocols without Public Coins using Modified Equality Queries

TL;DR

This paper introduces a quantum protocol compiler that transforms classical public-coin protocols into quantum protocols without public coins, enabling efficient solutions for various distributed computing problems.

Contribution

It presents the first general method to convert classical public-coin protocols into quantum protocols without public coins for multiple parties.

Findings

Quantum communication can replace public randomness without entanglement.

The compiler preserves communication complexity in the conversion.

Protocols for frequency moments and other problems are derived.

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.