Bell theorem without inequalities for two particles. II. Inefficient detectors

Daniel M. Greenberger, Michael Horne, Anton Zeilinger, and Marek Żukowski
Phys. Rev. A 78, 022111 – Published 22 August 2008

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.

  • Figure
  • Received 2 May 2008

DOI:https://doi.org/10.1103/PhysRevA.78.022111

©2008 American Physical Society

Authors & Affiliations

Daniel M. Greenberger

  • City College of New York, New York, New York 10031, USA

Michael Horne

  • Stonehill College, Easton, Massachusetts 02357, USA

Anton Zeilinger

  • Institute for Experimental Physics, University of Vienna, Vienna A-1090, Austria

Marek Żukowski

  • Institute for Theoretical Physics and Astrophysics, University of Gdansk, 80-952 Gdansk, Poland

See Also

Bell theorem without inequalities for two particles. I. Efficient detectors

Daniel M. Greenberger, Michael Horne, and Anton Zeilinger
Phys. Rev. A 78, 022110 (2008)

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Vol. 78, Iss. 2 — August 2008

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