  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.
