Guess your neighbour's input: a multipartite non-local game with no quantum advantage

TL;DR

This paper introduces a multipartite nonlocal game where quantum correlations do not outperform classical ones, but no-signalling correlations can, revealing new insights into the boundary between quantum and post-quantum correlations.

Contribution

It constructs a multipartite game demonstrating the limits of quantum advantage and explores the boundary between quantum and post-quantum correlations.

Findings

Quantum correlations do not outperform classical correlations in this game.

No-signalling correlations can outperform both classical and quantum correlations.

Some Bell inequalities correspond to facets of the local polytope.

Abstract

We present a multipartite nonlocal game in which each player must guess the input received by his neighbour. We show that quantum correlations do not perform better than classical ones at this game, for any prior distribution of the inputs. There exist, however, input distributions for which general no-signalling correlations can outperform classical and quantum correlations. Some of the Bell inequalities associated to our construction correspond to facets of the local polytope. Thus our multipartite game identifies parts of the boundary between quantum and post-quantum correlations of maximal dimension. These results suggest that quantum correlations might obey a generalization of the usual no-signalling conditions in a multipartite setting.