Fig. 1: Schematic representation of the correlations in multipartite Bell scenarios.
From: An elegant scheme of self-testing for multipartite Bell inequalities
This graphic is a schematic representation of the correlations in multipartite (involving arbitrary number N of spatially separated parties) Bell scenarios. Just like the bipartite Bell scenarios, the correlations which admit local hidden variable explanations form a convex polytope \({{{\mathcal{L}}}}\) (shiny blue small horizontal square), whose facets are the N-party MABK inequalities [Eq. (2)] (red edges). However, the convex set of biseparable quantum correlations \({{{{\mathcal{Q}}}}}_{N-1}\) (sky blue disk) does not form a polytope. Consequently, the linear inequalities such as the MABK [Eq. (2)] (pink edges of the large horizontal square) and Svetlichny inequalities [Eq. (3)] (green edges of the tilted square) do not form tight witness of genuine multipartite quantum non-locality. As the boundary of biseparable quantum correlations (black circle) is non-linear, Uffink’s quadratic inequalities [Eq. (4)] form tighter witnesses of genuine multipartite quantum non-locality.
