Ii. Nonlocality without Inequalities for Hardy States
نویسنده
چکیده
Hardy’s proof of “nonlocality without inequalities” [1] provides the simplest demonstration of Bell’s theorem [2] that there is no local realistic theory reproducing all predictions of quantum mechanics. Curiously, while the maximum violation of Bell inequalities occurs for maximally entangled states [3], Hardy’s proof does not go through for maximally entangled states. Recently, Wu, Xie, Huang, and Hsia (WXHH) [4] have claimed to have demonstrated nonlocality without inequalities for bipartite two-level systems prepared in a maximally entangled state. Their approach is based on a selection of events in a modified version of the two-particle interferometer proposed by Horne, Shimony, and Zeilinger [5]. In Sec. III of this paper WXHH’s approach is reexamined. I will argue that it fails to prove nonlocality without inequalities for maximally entangled states. After this analysis, it will become clear that no extension of Hardy’s proof to maximally entangled states is possible by selecting events before the local measurements involved in the proof. Therefore, it would be interesting to investigate whether such an extension can be achieved by using a set-up in which the selection of events necessarily occurs after the local measurements. In particular, I will investigate whether Hardy’s proof can be generalized by the replacement of one of the four von Neumann local measurements by a measurement to unambiguously discriminate between non-orthogonal states [6–9]. This scenario was consid-
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