Bell theorem involving all possible local measurements

The Bell theorem for a pair of two-state systems in a singlet state is formulated for the entire range of measurement settings. Typeset using REVTEX 1 The Bell theorem is usually formulated with the help of the Clauser-Horne [1] or the CHSH inequality [2]. These inequalities are satisfied by any local realistic theory and are violated by quantum mechanical predictions. They involve two apparatus settings at each of the two sides of the experiment. However, generalisation to more than two settings at each side are possible [3], [4], [5], [6]. There are several motivations for such generalisations. First of all new Bell inequalities may be more appropriate in some experimental situations, e.g., the chained Bell inequalities can reveal violation of local realism for the Franson type experiment [7]. Also, the academic question, why only two settings at each side, is that always necessary, is interesting in itself. Further, many of the currently performed quantum interferometric Bell tests did not involve stabilisation of the interferometers at specified settings optimal for the standard Bell