On the Limits of Quantum Multiparty Simultaneous Communication

2026-09-09

AI Summary

本文研究了多玩家同时通信模型中经典通信与量子通信的界限问题，通过Index Coordination游戏的泛化版本展示了量子通信在无共享纠缠或公共随机性情况下的局限。

Abstract

The Simultaneous Message Passing (SMP) model provides a fundamental framework for comparing classical and quantum communication. For two players, Gavinsky et al. (STOC 2006) established a separation underlying the incomparability of shared randomness and quantum communication: \textsc{Index Coordination} needs $O(\log n)$ public-coin bits but $Ω(n^{1/3})$ bounded-error qubits. In this work, we establish a multiparty exponential separation through $\operatorname{IC}_{k,n}$, a natural $k$-party generalization of \textsc{Index Coordination}. Public-coin protocols solve it unambiguously with maximum message length $O(\log n)$ bits. In contrast, quantum SMP protocols without shared entanglement or public coins require maximum message length $Ω(n^{1-1/k})$ qubits in the unambiguous regime and $Ω(n^{(k-1)/(k+1)})$ qubits in the bounded-error regime. A classical private-coin protocol matches the unambiguous bound, so quantum communication provides no asymptotic advantage over private randomness in this regime. For fixed error parameters, all constants are independent of $k$, establishing the exponential separation for every integer-valued function $k=k(n)\ge2$, without restricting its growth. Both quantum lower bounds become $Ω(n)$ when $k\ge c\log n$ for any fixed $c>0$, matching the full-input protocol and yielding tight linear complexity in both regimes. Our results demonstrate that quantum superposition cannot efficiently simulate the coordination afforded by public randomness, extending this separation to arbitrary $k$. To bound success probabilities for multiparty product states, we prove an exact factorization theorem for unambiguous quantum state identification, which may be of independent mathematical interest.

Problem

• Quantum Communication
• Simultaneous Message Passing
• Multiparty
• Index Coordination
• Public Randomness

Innovation

• Simultaneous Message Passing (SMP)
• quantum communication
• multiparty exponential separation
• unambiguous quantum state identification
• public randomness