Detector inefficiencies in the Einstein-Podolsky-Rosen experiment

The question of how to deal with inefficient detectors in actual experiments of the Einstein-Podolsky-Rosen type is studied. We derive the necessary and sufficient condition for compatibility with local realism of data collected in experiments with two settings of each detector, without making auxiliary assumptions about undetected events. For the conventional experiment with particles in the singlet state (or its photon analogue), the data predicted by the quantum theory do not violate this condition unless the quantum efficiency of the detectors exceeds 83%