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American Journal of Physics

Quantum mysteries revisited

N. David Mermin

Published Aug 1, 1990• 575 citations
Publisher

Abstract

A gedanken gadget is described, based on an idea of Greenberger, Horne, and Zeilinger, that provides a more powerful demonstration of quantum nonlocality than Bell’s analysis of the Einstein–Podolsky–Rosen experiment.
DOI
10.1119/1.16503

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Although considerable discussion about the completeness of quantum mechanics followed the publication in 1935 of the Gedanken experiment of Einstein, Podolsky, and Rosen (EPR), it was not until Bell's work, published in 3 965, that it was realized that the issue could be rigorously formulated and put to experimental test. An even more provocative demonstration of the incompatibility of quantum mechanics with local realism was recently discovered by Greenberger, Horne, and Zeilinger (GHZ) in a Gedanken experiment employing more than two particles.1 Typical of EPR experiments that have been proposed to date, one has a metastable system that decays into n particles.
It is shown that the Einstein-Podolsky-Rosen (EPR) correlations for arbitrary spin s and the Greenberger-Horne-Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the information Bell inequalities. Relations between the randomness, the nonlocality, and the entropic information for the EPR and the GHZ correlations are established and discussed.