Quantum advantages in multiparty communication

TL;DR

This work analyzes a two-sender, one-receiver multiparty communication task under two families of constraints: dimension-bounded and distinguishability-bounded. It characterizes the classical correlation polytope for $p(z|x,y)$ and demonstrates that quantum messages can outperform all classical strategies even without preshared entanglement or receiver input choices, using See-Saw optimization and a tailored SDP hierarchy to bound quantum performance. The authors provide explicit quantum strategies (qubits with specific state preparations and POVMs) that achieve violations for multiple facet inequalities across several $(n_x,n_y,n_z)$ configurations, and they compare these lower bounds with SDP upper bounds, observing convergence at higher dimensions. The results establish a clear quantum advantage in the constrained multiparty setting and offer a framework for bounding and exploring quantum correlations in more general network scenarios.

Abstract

We investigate two senders and one receiver multiparty communication scenario. Following Phys.Rev.A83, 062112 and arXiv : 2506.07699, we study multiparty communication bounded by dimension and distinguishability. We provide an explicit characterization of the classical correlations achievable under these constraints. We then demonstrate that quantum communication systematically exceeds these classical limits, even in the absence of preshared entanglement and without any input choice for the receiver. Furthermore, we implement semidefinite hierarchy tools tailored to the two-sender, one-receiver setting for both types of constraints considered. Our results reveal a clear quantum advantage in multiparty communication under those restrictions.

Figures (6)

• Figure 1: Caption
• Figure 2: $\mathcal{S_Q}$ and $\mathcal{S_Q}_d^L$ for $d=2,3,4,5$ of the inequality $\mathcal{I}_1$.
• Figure 3: $\mathcal{S_Q}$ and $\mathcal{S_Q}_d^L$ for $d=2,3,4,5$ of the inequality $\mathcal{I}_2$.
• Figure 4: $\mathcal{S_Q}$ and $\mathcal{S_Q}_d^L$ for $d=2,3,4,5$ of the inequality $\mathcal{I}_3$.
• Figure 5: $\mathcal{S_Q}$ and $\mathcal{S_Q}_d^L$ for $d=2,3,4,5$ of the inequality $\mathcal{I}_4$.