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

Abstract

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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Figure 1: Bell-test schematic and experimental realization.
Figure 2: Space–time analysis of the experiment.
Figure 3: Characterization of the set-up and the entangled state.
Figure 4: Loophole-free Bell inequality violation.

References

  1. 1

    Bell, J. S. On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)

    MathSciNet  Article  Google Scholar 

  2. 2

    Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Freedman, S. J. & Clauser, J. F. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    ADS  MathSciNet  Article  Google Scholar 

  5. 5

    Weihs, G., Jennewein, T., Simon, C., Weinfurter, H. & Zeilinger, A. Violation of Bell’s inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81, 5039–5043 (1998)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  6. 6

    Rowe, M. A. et al. Experimental violation of a Bell’s inequality with efficient detection. Nature 409, 791–794 (2001)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Matsukevich, D. N., Maunz, P., Moehring, D. L., Olmschenk, S. & Monroe, C. Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett. 100, 150404 (2008)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Scheidl, T. et al. Violation of local realism with freedom of choice. Proc. Natl Acad. Sci. USA 107, 19708–19713 (2010)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Hofmann, J. et al. Heralded entanglement between widely separated atoms. Science 337, 72–75 (2012)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Giustina, M. et al. Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227–230 (2013)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Christensen, B. G. et al. Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett. 111, 130406 (2013)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014)

    ADS  Article  Google Scholar 

  14. 14

    Garg, A. & Mermin, N. D. Detector inefficiencies in the Einstein-Podolsky-Rosen experiment. Phys. Rev. D 35, 3831–3835 (1987)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Eberhard, P. H. Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment. Phys. Rev. A 47, R747–R750 (1993)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Barrett, J., Collins, D., Hardy, L., Kent, A. & Popescu, S. Quantum nonlocality, Bell inequalities, and the memory loophole. Phys. Rev. A 66, 042111 (2002)

    ADS  Article  Google Scholar 

  17. 17

    Bell, J. S. Atomic-cascade photons and quantum-mechanical nonlocality. Comments Atom. Mol. Phys. 9, 121–126 (1980)

    CAS  Google Scholar 

  18. 18

    Żukowski, M., Zeilinger, A., Horne, M. A. & Ekert, A. K. “Event-ready-detectors” Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287–4290 (1993)

    ADS  Article  Google Scholar 

  19. 19

    Simon, C. & Irvine, W. T. M. Robust long-distance entanglement and a loophole-free Bell test with ions and photons. Phys. Rev. Lett. 91, 110405 (2003)

    ADS  Article  Google Scholar 

  20. 20

    Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    ADS  Article  Google Scholar 

  21. 21

    Gill, R. D. Time, finite statistics, and Bell’s fifth position. In Proc. Foundations of Probability and Physics 2 179–206 (Växjö Univ. Press, 2003)

    Google Scholar 

  22. 22

    Acín, A. et al. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)

    ADS  Article  Google Scholar 

  23. 23

    Colbeck, R. Quantum and Relativistic Protocols for Secure Multi-Party Computation. PhD thesis, Univ. Cambridge (2007); http://arxiv.org/abs/0911.3814

    Google Scholar 

  24. 24

    Pironio, S. et al. Random numbers certified by Bell’s theorem. Nature 464, 1021–1024 (2010)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Bell, J. S. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy 2nd edn (Cambridge Univ. Press, 2004)

    Google Scholar 

  26. 26

    Gerhardt, I. et al. Experimentally faking the violation of Bell’s inequalities. Phys. Rev. Lett. 107, 170404 (2011)

    ADS  Article  Google Scholar 

  27. 27

    Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Barrett, S. D. & Kok, P. Efficient high-fidelity quantum computation using matter qubits and linear optics. Phys. Rev. A 71, 060310 (2005)

    ADS  Article  Google Scholar 

  29. 29

    Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Abellan, C., Amaya, W., Mitrani, D., Pruneri, V. & Mitchell, M. W. Generation of fresh and pure random numbers for loophole-free Bell tests. Preprint available at http://arxiv.org/abs/1506.02712

  31. 31

    Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987)

    ADS  CAS  Article  Google Scholar 

  32. 32

    Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

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.

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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.

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Correspondence to R. Hanson.

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The authors declare no competing financial interests.

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Hensen, B., Bernien, H., Dréau, A. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015). https://doi.org/10.1038/nature15759

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