A new way to obtain Bell inequalities

Bell proved in 1965 [ 1 ] that nonlocality is an unavoidable property of quantum theory. By assuming locality, he derived a set of inequalities which, he then showed. are violated by the predictions of quantum theory. Since then a number of different Bell inequalities have been discovered, the most important of these are the Clauser, Horne, Shimony, and Holt (CHSH ) inequalities [ 21 derived in 1969 and the Clauser and Horne inequalities [ 3 ] derived in 1974. Whilst all of these inequalities demonstrate the contradiction between quantum mechanics and local realism, an intuitive understanding of the contradiction is lost in the mathematics of their proofs. For this reason the recent demonstration of a more direct contradiction between quantum mechanics and local realism by Greenberger, Horne, and Zeilinger (GHZ) [4] and Mermin [5] (see also ref. [6]) where inequalities are not necessary has caused much interest. It is not only that these contradictions do not involve inequalities that makes them appealing but also that they provide an immediate and obvious contradiction between quantum mechanics and local realism. Unfortunately, this approach only works for three or more measurements#’ whereas we are more