Maximal violation of Bell's inequality in the case of real experiments

Einstein's locality is invoked to derive a correlation inequality. In the case of ideal experiments, this inequality is equivalent to Bell's original inequality of 1965 which, as is well known, is violated by a maximum factor of 1.5. The crucial point is that even in the case of real experiments where polarizers and detectors are non-ideal, the present inequality is violated by a factor of 1.5, whereas previous inequalities such as Clauser-Horne-Shimony-Holt inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a factor of $\sqrt 2$. The larger magnitude of violation can be of importance for the experimental test of locality. Moreover, the supplementary assumption used to derive this inequality is weaker than Garuccio-Rapisarda assumption. Thus an experiment based on this inequality refutes a larger family of hidden variable theories than an experiment based on Garuccio-Rapisarda inequality.