Possibilities Determine the Combinatorial Structure of Probability Polytopes

Abstract

We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, given by linear equations together with non-negativity constraints on the variables.

References in corpus (2)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Extremal correlations of the tripartite no-signaling polytope

Cited by in corpus (7)

• Graph-theoretic strengths of contextuality
• Consequences and applications of the completeness of Hardy's nonlocality
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• The Sheaf-Theoretic Structure of Definite Causality
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• Connecting extended Wigner's friend arguments and noncontextuality
• Convexity of noncontextual wirings and how they order the set of correlations