Letter | Published:

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

Nature volume 526, pages 682686 (29 October 2015) | Download Citation


More than 50 years ago1, John Bell proved that no theory of nature that obeys locality and realism2 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 reported3,4,5,6,7,8,9,10,11,12,13; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in ‘loopholes’13,14,15,16. 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 scheme17,18,19 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 (detection loophole14,15), 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 conditions13. 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 memory16,21 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 communication22 and randomness certification23,24.

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We thank A. Acín, A. Aspect, P. Bierhorst, A. Doherty, R. Gill, P. Grünwald, M. Giustina, L. Mancinska, J. E. Mooij, T. Vidick, H. Weinfurter and Y. Zhang for discussions and/or reading our manuscript, and M. Blauw, P. Dorenbos, R. de Stefano, C. Tiberius, T. Versluis, R. Zwagerman and Facilitair Management and Vastgoed for help with the realization of the laboratories and the optical fibre connections. We acknowledge support from the Dutch Organization for Fundamental Research on Matter (FOM), the Dutch Technology Foundation (STW), the Netherlands Organization for Scientific Research (NWO) through a VENI grant (T.H.T.) and a VIDI grant (S.W.), the Defense Advanced Research Projects Agency QuASAR program, the Spanish MINECO project MAGO (reference FIS2011-23520) and Explora Ciencia (reference FIS2014-62181-EXP), the European Regional Development Fund (FEDER) grant TEC2013-46168-R, Fundacio Privada CELLEX, FET Proactive project QUIC and the European Research Council through projects AQUMET and HYSCORE.

Author information

Author notes

    • H. Bernien

    Present address: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.


  1. QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands

    • B. Hensen
    • , H. Bernien
    • , A. E. Dréau
    • , A. Reiserer
    • , N. Kalb
    • , M. S. Blok
    • , J. Ruitenberg
    • , R. F. L. Vermeulen
    • , R. N. Schouten
    • , D. Elkouss
    • , S. Wehner
    • , T. H. Taminiau
    •  & R. Hanson
  2. Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands

    • B. Hensen
    • , H. Bernien
    • , A. E. Dréau
    • , A. Reiserer
    • , N. Kalb
    • , M. S. Blok
    • , J. Ruitenberg
    • , R. F. L. Vermeulen
    • , R. N. Schouten
    • , T. H. Taminiau
    •  & R. Hanson
  3. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

    • C. Abellán
    • , W. Amaya
    • , V. Pruneri
    •  & M. W. Mitchell
  4. ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

    • V. Pruneri
    •  & M. W. Mitchell
  5. Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK

    • M. Markham
    •  & D. J. Twitchen


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B.H., H.B. and R.H. devised the experiment. B.H., H.B., A.E.D., A.R., M.S.B., J.R., R.F.L.V. and R.N.S. built and characterized the experimental set-up. M.W.M., C.A. and V.P. designed the quantum random-number generators (QRNGs), M.W.M. and C.A. designed the randomness extractors, and W.A. and C.A. built the interface electronics and the QRNG optics, the latter with advice from V.P. C.A. and M.W.M. designed and implemented the QRNG statistical metrology. C.A. designed and implemented the QRNG output tests. M.M. and D.J.T. grew and prepared the diamond device substrates. H.B. and M.S.B. fabricated the devices. B.H., H.B., A.E.D., A.R. and N.K. collected and analysed the data, with support from T.H.T. and R.H. D.E. and S.W. performed the theoretical analysis. B.H., A.R., T.H.T., D.E., S.W. and R.H. wrote the manuscript. R.H. supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to R. Hanson.

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    Supplementary Information

    This file contains Supplementary Text and Data, Supplementary Figures 1-7, Supplementary Table 1 and additional references.

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