Nonlocality without inequalities has not been proved for maximally entangled states

Two approaches to extend Hardy’s proof of nonlocality without inequalities to maximally entangled states of bipartite two-level systems are shown to fail. On one hand, it is shown that the proof of Wu and co-workers [Phys. Rev. A 53, R1927 (1996)] uses an effective state which is not maximally entangled. On the other hand, it is demonstrated that Hardy’s proof cannot be generalized by the replacement of one of the four von Neumann measurements involved in the original proof by a generalized measurement to unambiguously discriminate between nonorthogonal states.