Scalable and perfect noise-robust communication with no multipartite quantum entanglement

Abstract

Recently, Chakraborty et al. considered a distributed computing scenario in which multiple senders and a single computing server compute a specific global function of their input strings [Phys. Rev. A 111(3), 032617 (2025)]. They demonstrated that when the senders and the server share a multipartite Greenberger–Horne–Zeilinger (GHZ) state, the classical communication overhead can be reduced by $n-1$ bits for $n$ senders in contrast to the scenario without entanglement. However, the depth requirements of unitary circuits for GHZ state preparation, as well as the unreliable long-distance distribution of GHZ states, limit the practical applications of these distributed computing tasks under current conditions. Here, we propose a feasible distributed computing protocol that does not require multipartite entangled states. We analyze the performance of our protocol under certain types of noise. We demonstrate that our protocol has a unique advantage: it exhibits perfect robustness under these types of noise. In addition, in contrast to the GHZ-state-based protocol, which requires one bit of classical communication from each sender, our protocol eliminates the need for classical communication. Moreover, this advantage can scale arbitrarily as the number of senders increases. Our proposal provides an important pathway for practical communication complexity tasks.