Bell inequalities define constraints on probability distributions for bipartite systems under the assumptions of locality and realism, characterizing the classical region as a convex polytope within state space. The core principle establishes that any probabilistic model expressible as a convex combination of local deterministic configurations must satisfy specific linear bounds derived from the polar of this polytope; violation of these bounds indicates non-local quantum correlations such as entanglement. This concept belongs to the domain of foundational quantum mechanics and information theory, providing the mathematical framework for distinguishing classical hidden variable theories from intrinsically quantum mechanical behaviors via observable correlators like those in the CHSH inequality.
Bell inequalities define constraints on probability distributions for bipartite systems under the assumptions of locality and realism, characterizing the classical region as a convex polytope within …