Formalizing Bell Nonlocality

Abstract

This chapter covers the essential mathematical tools for the study of nonlocality. It begins with the main object under study: a collection of several probability distributions usually called “behavior”. The crucial definition of locality is then given, followed by Fine’s theorem that relates local behaviors to pre-existing values and clarifies the role of local deterministic processes. In turn, one finds that local behaviors belong to a polytope, whose facets are Bell inequalities. The simplest scenario, called CHSH, is studied in detail.