Possibilities Determine the Combinatorial Structure of Probability Polytopes

TL;DR

This paper demonstrates that the combinatorial structure of no-signalling probability polytopes is fully determined by the support of the models, revealing a fundamental link between possibilistic information and polytope structure.

Contribution

It establishes that the combinatorial structure of certain polytopes in quantum information is completely characterized by their support, generalizing to all polytopes in standard form.

Findings

The structure of no-signalling polytopes is determined by support.

Possibilistic support fully characterizes polytope combinatorics.

Generalization to all polytopes in standard form.

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.