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 CHSHK and the success probability PK associated with Hardy's ladder test of nonlocality for two qubits and K+1 observables per qubit. Then, by invoking the Tsirelson bound for CHSHK, the derived relationship allows us to establish an upper limit on PK. In addition, we draw the connection between CHSHK and the chained version of the Clauser-Horne (CH) inequality.

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