Significance of an experiment of the Greenberger-Horne-Zeilinger kind

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Abstract
Restrictive conditions on the class of allowed physical theories are drawn from the assumption that the predictions of quantum theory are valid for an experiment of the kind proposed by Greenberger, Horne, and Zeilinger [in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, 1989)]. It is shown that no theory can be compatible with the following four conditions. (1) The choices to be made by the three experimenters can be treated, in this context, as three independent free variables. (2) For each of the six possible local measurements under consideration, if that local measurement were to be performed, then exactly one of the alternative possible outcomes of this measurement must be selected as the actual outcome. (3) For each triad of measurements in a certain set of possible triads, if that triad were to be performed, then the corresponding triad of selected outcomes must satisfy the correlation condition predicted by quantum theory. (4) For each of the six possible local measurements, if that local measurement were to be performed, then the selected outcome must, according to the theory, be independent of which two experiments will later, in some frame of reference, be performed in the other two regions.

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