Geometric interpretation of the CHSH inequality of nonmaximally entangled states

TL;DR

This paper presents a geometric approach to understanding the CHSH inequality for both pure and mixed bipartite states, linking entanglement to a perimeter maximization problem to identify optimal measurements.

Contribution

It introduces a novel geometric interpretation of the CHSH inequality applicable to non-maximally entangled states, enabling determination of optimal measurement settings.

Findings

Geometric representation simplifies CHSH analysis

Optimal measurements derived from perimeter maximization

Applicable to pure and mixed entangled states

Abstract

We show that for pure and mixed states the problem of maximizing the correlation measure in the CHSH inequality reduces to maximizing the perimeter of a parallelogram enclosed by an ellipse characterized by the entanglement contained in the bipartite system. Since our geometrical description is also valid for a non-maximally entangled state we can determine the corresponding optimal measurements.