Extremal correlations of the tripartite no-signaling polytope

TL;DR

This paper classifies the extremal points of the tripartite no-signaling polytope with two inputs and outputs, revealing 53856 extremal points in 46 classes, and explores their implications for non-locality and Bell inequalities.

Contribution

It provides the first comprehensive classification of extremal points of the tripartite no-signaling polytope with detailed analysis of their properties.

Findings

Identified 53856 extremal points in 46 classes.

Linked extremal points to multipartite non-locality.

Discussed the relation to Bell inequalities.

Abstract

The no-signaling polytope associated to a Bell scenario with three parties, two inputs, and two outputs is found to have 53856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to various definitions of multipartite non-locality and briefly discuss other issues like the interconversion between extremal points seen as a resource and the relation of the extremal points to Bell-type inequalities.