Quantum communication complexity beyond Bell nonlocality

TL;DR

This paper explores the connection between quantum communication complexity and generalized nonlocality, demonstrating a quantum advantage in multipartite tasks using GHZ states and establishing new Bell-like inequalities.

Contribution

It introduces a novel framework linking quantum CCPs with generalized nonlocality, extending beyond Bell's theorem, and experimentally demonstrates quantum advantage with multipartite states.

Findings

Quantum advantage demonstrated with GHZ states in a multipartite CCP

New Bell-like inequalities linked to quantum CCPs

Experimental validation of quantum communication benefits

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 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.