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http://www.nature.com/nature/journal/vaop/ncurrent/full/nature15759.html

Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres

B. Hensen,

H. Bernien,

A. E. Dréau,

A. Reiserer,

N. Kalb,

M. S. Blok,

J. Ruitenberg,

R. F. L. Vermeulen,

R. N. Schouten,

C. Abellán,

W. Amaya,

V. Pruneri,

M. W. Mitchell,

M. Markham,

D. J. Twitchen,

D. Elkouss,

S. Wehner,

T. H. Taminiau

& R. Hanson

Nature (2015) doi:10.1038/nature15759 Received 19 August 2015 Accepted 28 September 2015 Published online 21 October 2015

More than 50 years ago, John Bell proved that no theory of nature that obeys

locality and realism can reproduce all the predictions of quantum theory: in

any local-realist theory, the correlations between outcomes of measurements on

distant particles satisfy an inequality that can be violated if the particles

are entangled. Numerous Bell inequality tests have been reported however, all

experiments reported so far required additional assumptions to obtain a

contradiction with local realism, resulting in ‘loopholes’. Here we report a

Bell experiment that is free of any such additional assumption and thus directly

tests the principles underlying Bell’s inequality. We use an event-ready

scheme that enables the generation of robust entanglement between

distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin

read-out avoids the fair-sampling assumption, while the use of fast random-basis

selection and spin read-out combined with a spatial separation of 1.3 kilometres

ensure the required locality conditions. We performed 245 trials that tested the

CHSH–Bell inequality20 S = 2 and found S = 2.42 ± 0.20 (where S quantifies the

correlation between measurement outcomes). A null-hypothesis test yields a

probability of at most P = 0.039 that a local- realist model for space-like

separated sites could produce data with a violation at least as large as we

observe, even when allowing for memory in the devices. Our data hence imply

statistically significant rejection of the local-realist null hypothesis. This

conclusion may be further consolidated in future experiments; for instance,

reaching a value of P = 0.001 would require approximately 700 trials for an

observed S = 2.4. With improvements, our experiment could be used for testing

less-conventional theories, and for implementing device-independent quantum-

secure communication and randomness certification.

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