Chained Clauser-Horne-Shimony-Holt inequality for Hardy's ladder test of nonlocality

TL;DR

This paper derives a precise relationship between chained Bell inequalities and Hardy's ladder test of nonlocality, establishing bounds on success probabilities using non-signaling and Tsirelson's bounds for two-qubit systems.

Contribution

It introduces an exact relationship between chained CHSH inequalities and Hardy's ladder test, linking nonlocality measures with non-signaling principles and Tsirelson bounds.

Findings

Derived the relationship between CHSH_K and P_K.

Established an upper limit on Hardy's ladder success probability.

Connected CHSH_K with chained CH inequalities.

Abstract

Relativistic causality forbids superluminal signaling between distant observers. By exploiting the non-signaling principle, we derive the exact relationship between the chained Clauser-Horne-Shimony-Holt sum of correlations CHSH_K and the success probability P_K associated with Hardy's ladder test of nonlocality for two qubits and K+1 observables per qubit. Then, by invoking the Tsirelson bound for CHSH_K, the derived relationship allows us to establish an upper limit on P_K. In addition, we draw the connection between CHSH_K and the chained version of the Clauser-Horne (CH) inequality.