Nonlocality without inequalities for almost all entangled states for two particles

We provide a streamlined proof of Hardy’s theorem, that almost every entangled state for a pair of quantum particles admits a ‘‘proof of nonlocality’’ without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy’s assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.