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Phys Rev Lett. 2011 Mar 11;106(10):100406. Epub 2011 Mar 10.

How much measurement independence is needed to demonstrate nonlocality?

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


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.

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