The geometric link between Hardy and Clauser-Horne-Shimony-Holt

TL;DR

This paper reveals a geometric connection between Hardy nonlocality and CHSH inequality violation, showing Hardy's condition as an optimization problem involving triangle side lengths under specific constraints.

Contribution

It establishes a novel geometric interpretation linking Hardy nonlocality to CHSH violation, extending the understanding of quantum nonlocality conditions.

Findings

Hardy condition is equivalent to a triangle side length optimization.

The geometric approach clarifies the effects of different constraints.

Hardy nonlocality can be viewed as an optimized length difference in a geometric figure.

Abstract

We show that the Hardy nonlocality condition is equivalent to the violation of the CHSH inequality with additional constraints. We adapt the geometrical optimization of the violation of the CHSH inequality to these additional constraints and show that the Hardy condition is equivalent to optimizing the length difference of two sides in a triangle. Furthermore, we discuss the effects of the different constraints.