A Bell Theorem Without Inequalities for Two Particles, Using Inefficient Detectors

Details A Bell Theorem Without Inequalities for Two Particles, Using Inefficient Detectors A Bell Theorem Without Inequalities for Two Particles, Using Inefficient Detectors

2005-10-27

arxiv.org/abs/quant-ph/0510207v2

Physics

Quantum Physics

21 pages, 1 embedded figure. This is a companion paper to quant-ph/0510201v2 There are major changes in this paper. There is a

Scientific paper

We again consider (as in a companion paper) an entangled two-particle state that is produced from two independent down-conversion 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 don't 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 (GHZ) 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.

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