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