Geometric link between the Hardy nonlocality condition and the Clauser-Horne-Shimony-Holt inequality

We show that the Hardy nonlocality condition is equivalent to the violation of the Clauser-Horne-Shimony-Holt (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.

Automated summary

This research demonstrates the equivalence between the Hardy nonlocality condition and the violation of the CHSH inequality alongside additional constraints. By adapting the geometrical optimization approach, the study reveals that the Hardy condition can be represented as optimizing the length difference between two sides of a triangle. Moreover, the effects of different constraints are discussed.