Consequences of recent loophole-free experiments on a relaxation of measurement independence

Abstract

Recent experiments using innovative optical detectors and techniques have strongly increased the capacity of testing the violation of the Bell´s inequalities in Nature. Most of them have used the Eberhard´s inequality (EI) to close the "detection" loophole. Closing the "locality" loophole has been attempted by spacelike separated detections and fast changes of the bases of observation, driven by random number generators of new design. Also, pulsed pumping and time-resolved data recording to close the "time-coincidence" loophole, and sophisticated statistical methods to close the "memory" loophole, have been used. In this paper, the meaning of the EI is reviewed. A simple hidden variables theory based on a relaxation of the condition of "measurement independence," which was devised long ago for the Clauser-Horne-Shimony and Holt inequality, is adapted to the EI case. It is used here to evaluate the significance of the results of the recent experiments, which are briefly described. A table summarizes the main results.