Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres.
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 (detection loophole), 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 inequality 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.
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Hensen
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Bernien
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Dréau
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Reiserer
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Kalb
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Blok
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Ruitenberg
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Vermeulen
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Schouten
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
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Abellán
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
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Amaya
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain.
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Pruneri
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain.
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Mitchell
Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK.
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Markham
Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK.
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Twitchen
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Elkouss
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Wehner
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Taminiau
QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Hanson