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

We consider 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 prove a Greenberger-Horne-Zeilinger (GHZ) type theorem, showing that the quantum mechanical perfect correlations for such a state are inconsistent with any deterministic, local, realistic theory. This theorem holds for individual events with no inequalities, for detectors of 100% efficiency.