Abstract
We again consider (as in a companion paper) an entangled two-particle state that is produced from two independent downconversion sources by the process of ``entanglement swapping,'' so that the particles have never met. We show that there is a natural extension of the Einstein-Pololsky-Rosen discussion of ``elements of reality'' to include inefficient detectors. We consider inefficient deterministic, local, realistic models of quantum theory that are ``robust,'' which we consider to be the minimum requirement for them to be taken seriously. By robust, we mean they satisfy the following three criteria: (a) they reproduce the quantum results for perfect correlations, if all particles are detected; (b) they produce some counts for every setting of the angles (so they do not describe some experiments that can easily be performed as ``impossible''); (c) all their hidden variables are relevant (they must each produce a detectable result in some experiment). For such models, we prove a Greenberger-Horne-Zeilinger type theorem for arbitrary detection efficiencies, showing that any such theory is inconsistent with the quantum-mechanical perfect correlations. This theorem holds for individual events with no inequalities. As a result, the theorem is also independent of any random sampling hypothesis, and we take it as a refutation of such realistic theories, free of the detection efficiency and random sampling ``loopholes.'' The hidden variable analysis depends crucially on the use of two independent laser sources for the downconversions. We also investigate the necessity of using two independent sources versus a single source for all particles. Finally, we argue that the state we use can legitimately be considered as a two-particle state, and used as such in experiments.
Published Version
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