By Joseph Ho, George Moreno, Samuraí Brito, Francesco Graffitti, Christopher L. Morrison, Ranieri Nery, Alexander Pickston, Massimiliano Proietti, Rafael Rabelo, Alessandro Fedrizzi, Rafael Chaves.
Submitted to arXiv on 11 June 2021.
Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks such as parallel computation and circuit optimisation. Crucially, the communication overhead introduced by the allotment process should be minimised — a key motivation behind the communication complexity problem (CCP). Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. Furthermore, the connection between quantum CCPs and nonlocality provides an information-theoretic insights into fundamental quantum mechanics. Here we connect quantum CCPs with a generalised nonlocality framework — beyond the paradigmatic Bell’s theorem — by incorporating the underlying causal structure, which governs the distributed task, into a so-called nonlocal hidden variable model. We prove that a new class of communication complexity tasks can be associated to Bell-like inequalities, whose violation is both necessary and sufficient for a quantum gain. We experimentally implement a multipartite CCP akin to the guess-your-neighbour-input scenario, and demonstrate a quantum advantage when multipartite Greenberger-Horne-Zeilinger (GHZ) states are shared among three users.