Entanglement-based quantum communication complexity beyond Bell nonlocality

Abstract 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 allotment process should be minimised—a key motivation behind complexity problem (CCP). Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. Furthermore, connection between quantum CCPs non-locality provides an information-theoretic insight into fundamental mechanics. Here we connect with generalised framework—beyond Bell’s paradigmatic theorem—by incorporating underlying causal structure, which governs so-called non-local hidden-variable model. We prove new class of tasks associated Bell-like inequalities, whose violation is both necessary sufficient gain. experimentally implement multipartite CCP akin guess-your-neighbour-input scenario, demonstrate advantage when Greenberger-Horne-Zeilinger (GHZ) states shared among three users.