Is Communication Complexity Physical?

TL;DR

This paper supports the conjecture that the limits of quantum correlations are linked to communication complexity, showing that hypothetical stronger non-locality would trivialize multipartite communication problems.

Contribution

It extends the conjecture to multipartite scenarios, demonstrating that increased non-locality would render all communication complexity problems trivial.

Findings

Multipartite problems reduce to triviality with increased non-locality.

The nonlocal-box used relates to a generalized Bell inequality.

Supports the physicality of quantum correlations in communication complexity.

Abstract

Recently, Brassard et. al. conjectured that the fact that the maximal possible correlations between two non-local parties are the quantum-mechanical ones is linked to a reasonable restriction on communication complexity. We provide further support for the conjecture in the multipartite case. We show that any multipartite communication complexity problem could be reduced to triviality, had Nature been more non-local than quantum-mechanics by a quite small gap for any number of parties. Intriguingly, the multipartite nonlocal-box that we use to show the result corresponds to the generalized Bell inequality that manifests maximal violation in respect to a local hidden-variable theory.