How Much Measurement Independence Is Needed to Demonstrate Nonlocality?

Jonathan Barrett and Nicolas Gisin
Phys. Rev. Lett. 106, 100406 – Published 10 March 2011

Abstract

If nonlocality is to be inferred from a violation of Bell’s inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We demonstrate a connection between models that weaken this assumption, allowing partial correlation, and (i) models that allow classical communication between the distant parties, (ii) models that exploit the detection loophole. Even if Bob’s choices are completely independent, all correlations from projective measurements on a singlet can be reproduced, with mutual information between Alice’s choice and local variables less than or equal to one bit.

  • Figure
  • Received 13 September 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.100406

© 2011 American Physical Society

Authors & Affiliations

Jonathan Barrett

  • Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom

Nicolas Gisin

  • Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland

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Vol. 106, Iss. 10 — 11 March 2011

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