title: Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis.
abstract: The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: B
authors: B
authors: Hensen
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: N
authors: N
authors: Kalb
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: M S
authors: MS
authors: Blok
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: A E
authors: AE
authors: Dréau
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: A
authors: A
authors: Reiserer
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: R F L
authors: RF
authors: Vermeulen
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: R N
authors: RN
authors: Schouten
authors: Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX110QR, United Kingdom.
authors: M
authors: M
authors: Markham
authors: Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX110QR, United Kingdom.
authors: D J
authors: DJ
authors: Twitchen
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: K
authors: K
authors: Goodenough
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: D
authors: D
authors: Elkouss
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: S
authors: S
authors: Wehner
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: T H
authors: TH
authors: Taminiau
authors: QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience Delft, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands.
authors: R
authors: R
authors: Hanson