Fair-sampling assumption is not necessary for testing local realism

Dominic W. Berry, Hyunseok Jeong, Magdalena Stobińska, and Timothy C. Ralph
Phys. Rev. A 81, 012109 – Published 13 January 2010

Abstract

Almost all Bell inequality experiments to date have used postselection and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorizes as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson’s bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson’s bound to be violated while the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality still holds for unentangled states, and present an experimentally feasible example.

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  • Received 15 May 2009

DOI:https://doi.org/10.1103/PhysRevA.81.012109

©2010 American Physical Society

Authors & Affiliations

Dominic W. Berry1,2, Hyunseok Jeong3,4, Magdalena Stobińska3,5,6, and Timothy C. Ralph3

  • 1Centre for Quantum Computer Technology, Macquarie University, Sydney, NSW 2109, Australia
  • 2Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada
  • 3Centre for Quantum Computer Technology, Department of Physics, The University of Queensland, St Lucia, Qld 4072, Australia
  • 4Center for Subwavelength Optics, Department of Physics and Astronomy, Seoul National University, Seoul, 151-742, Korea
  • 5Institut für Optik, Information und Photonik, Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
  • 6Institute of Theoretical Physics and Astrophysics, University of Gdańsk, ul. Wita Stwosza 57, PL-80-952 Gdańsk, Poland

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Issue

Vol. 81, Iss. 1 — January 2010

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