Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
B. Hensen,1, 2 H. Bernien,1, 2, ∗ A.E. Dr´eau,1, 2 A. Reiserer,1, 2 N. Kalb,1, 2 M.S. Blok,1, 2 J. Ruitenberg,1, 2 R.F.L. Vermeulen,1, 2 R.N. Schouten,1, 2 C. Abell´an,3 W. Amaya,3 V. Pruneri,3 M.W. Mitchell,3, 4 M. Markham,5 D.J. Twitchen,5 D. Elkouss,1 S. Wehner,1 T.H. Taminiau,1, 2 and R. Hanson1, 2, †
1QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands 2Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands 3 ICFO-Institut de Ciencies Fotoniques, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain. 4 ICREA-Instituci´o Catalana de Recerca i Estudis Avanats, Lluis Companys 23, 08010 Barcelona, Spain 5Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX110QR, United Kingdom.
For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality1 . In his seminal work2 , John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, numerous ingenious Bell inequality tests have been reported3-12. However, because of experimental limitations, all experiments to date required additional assumptions to obtain a contradiction with local realism, resulting in loopholes12-15. Here we report on a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell’s inequality. We employ an event-ready scheme2,16,17 that enables the generation of high-fidelity entanglement between distant electron spins. Efficient spin readout avoids the fair sampling assumption (detection loophole13,14), while the use of fast random basis selection and readout combined with a spatial separation of 1.3 km ensure the required locality conditions12. We perform 245 trials testing the CHSH-Bell inequality18 S ≤ 2 and find S = 2.42 ± 0.20. A null hypothesis test yields a probability of p = 0.039 that a local-realist model for space-like separated sites produces data with a violation at least as large as observed, even when allowing for memory15,19 in the devices. This result rules out large classes of local realist theories, and paves the way for implementing device-independent quantum-secure communication20 and randomness certification21,22 .
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