Chained Clauser–Horne–Shimony–Holt inequality for Hardy’s ladder test of nonlocality

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.

Cabello’s nonlocality for generalized three-qubit GHZ states

“…Table 1 lists P max K and C max K for K = 1 to 10. Furthermore, as K → ∞, both P max K and C max K tend to 0.5, which is the maximum allowed value within GNST for any given K [36,37]. Finally, it is to be mentioned that Chen et al [38] found a generalization of HNA applicable to high dimensional bipartite quantum systems.…”