Scalable & Noise-Robust Communication Advantage of Multipartite Quantum Entanglement

TL;DR

The paper tackles distributed computation with $n$ senders and a single receiver, showing that sharing an $(n+1)$-qubit GHZ state yields a scalable quantum advantage: Bob can compute the global function $f_n$ with only $1$ bit from each sender, while classical protocols require more, yielding a $(n-1)$-bit reduction in communication overhead. The authors analyze the protocol's robustness to white noise via $G^{(p)}_{n+1}$ and establish tight classical success bounds $P^n_{ ext{R}}$ in the absence of entanglement, contrasting them with quantum success $P_{ Q}=(2-p)/2$. They further connect the perfect advantage to Mermin-type pseudo-telepathy games and discuss experimental prospects and self-testing avenues to certify the required multipartite entanglement. Overall, the work demonstrates a scalable, noise-tolerant quantum advantage in multipartite communication complexity and outlines concrete paths toward experimental realization. $f_n=igoplus_{i=1}^n x_i^1 igoplus y^1 igoplus ext{P}igl[( extstyleigoplus_{i=1}^n x_i^0 + y^0)/2igr]$ and the protocol leveraging $|G_{n+1} angle$ are central to achieving this advantage.

Abstract

Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing inter-server communication -- an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multi-qubit Greenberger-Horne-Zeilinger (GHZ) state -- a quintessential form of genuine multipartite entanglement -- certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by (n-1) bits for n senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this novel quantum advantage.

Figures (2)

• Figure 1: Impossibility of evaluating $f_n$ in $\overline{\mathrm{CC}}_n$ scenario implies impossibility of evaluating $f_n$ in $\mathrm{CC}_n$ scenario, for any $\alpha$ channels.
• Figure 2: Noise tolerance of entanglement-based protocol: We consider the white noise model for noisy GHZ states, defined as $G^{(p)}_{n+1} := (1-p)\ket{G_{n+1}}\bra{G_{n+1}} + p(\mathbb{I}_2/2)^{\otimes n+1}$. These states are fully separable if and only if $1/[1 + 2^{-n}] \leq p \leq 1$, and they remain genuinely multipartite entangled if and only if $0 \leq p < 1/[2 - 2^{-n}]$Dur2000(1)Schack2000Guhne2010. For any $n>2$, the states provide an advantage in the corresponding $\mathrm{CC_n}$ task for $p \in [0,1/2]$. For $n=2$ and $n=3$, this advantage is not possible for $p > 1/2$. However, for larger $n$, such possibilities are not excluded, and the quantum protocol may exhibit greater noise robustness. Furthermore, robustness analysis of the quantum protocol can also be extended to colored noise models.

Theorems & Definitions (10)

• Theorem 1
• proof
• Theorem 2
• proof
• Proposition 1
• proof
• Theorem 3
• proof
• Theorem 4
• proof