Revisited aspects of the local set in CHSH Bell scenario

TL;DR

This paper provides a new, geometrically intuitive description of the local polytope and its facets in the CHSH Bell scenario, enhancing understanding of quantum correlations and local realism.

Contribution

It offers a constructive and geometric approach to analyzing the local set in the CHSH Bell scenario, which is a novel perspective compared to previous algebraic methods.

Findings

Detailed geometric characterization of the local polytope.

Identification of facets and their significance in Bell inequalities.

Enhanced understanding of local realism in bipartite quantum systems.

Abstract

The Bell inequalities stand at the cornerstone of the developments of quantum theory on both the foundational and applied side. The discussion started as a way to test whether the quantum description of reality is complete or not, but it developed in such a way that a new research area stemmed from it, namely quantum information. Far from being and exhausted topic, in the present paper we present a constructive and geometrically intuitive description of the local polytope and its facets in a bipartite Bell scenario with two dichotomic measurements per party.