Ja. Larsson et J. Semitecolos, Strict detector-efficiency bounds for n-site Clauser-Horne inequalities - art. no. 022117, PHYS REV A, 6302(2), 2001, pp. 2117
An analysis of detector-efficiency in many-site Clauser-Horne inequalities
is presented for the case of perfect visibility. It is shown that there is
a violation of the presented n-site Clauser-Horne inequalities if and only
if the efficiency is greater than n/(2n - 1). Thus, for a two-site two-sett
ing experiment there are no quantum-mechanical predictions that violate loc
al realism unless the efficiency is greater than 2/3. Second, there are n-s
ite experiments for which the quantum-mechanical predictions violate local
realism whenever the efficiency exceeds 1/2.