Strict detector-efficiency bounds for n-site Clauser-Horne inequalities

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-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than 23. Second, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds 12.