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.

翻译：本文研究多方同时消息传递（SMP）模型的量子版本，证明在某些情况下量子通信可以替代公共随机性，且无需各参与方共享纠缠态。这一结论在双参与者场景中已被证实，但对于三方及以上参与者的情形此前仅存在负面结果。我们的核心技术贡献在于提出一种编译器，可将任何基于"改进型相等查询"的经典公共硬币同时协议，转化为具有相近通信复杂度的无公共硬币量子同时协议。基于该编译器，我们进一步推导出适用于频率矩计算、邻域多样性分析、孤立团枚举等多个问题的具体协议方案。