Loophole-free Bell test using electron spins in diamond
Second experiment and additional analysis
Bas Hensen (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QID/Hanson Lab)
Norbert Kalb (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QID/Hanson Lab)
Machiel Blok (TU Delft - QuTech Advanced Research Centre, TU Delft - QN/Quantum Transport, Kavli institute of nanoscience Delft)
Anaïs Dréau (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - QID/Hanson Lab)
Andreas Reiserer (TU Delft - QID/Hanson Lab, TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft)
Raymond Vermeulen (TU Delft - ALG/General, Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre)
Raymond Schouten (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - ALG/General)
M. Markham (Element Six Innovation)
D.J. Twitchen (Element Six Innovation)
Kenneth Goodenough (TU Delft - QuTech Advanced Research Centre, TU Delft - QID/Wehner Group)
David Elkouss Coronas (TU Delft - QuTech Advanced Research Centre, TU Delft - Quantum Information and Software, TU Delft - QID/Wehner Group)
Stephanie Wehner (TU Delft - Quantum Internet Division, TU Delft - Quantum Information and Software, TU Delft - QuTech Advanced Research Centre)
Tim Taminiau (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QID/Taminiau Lab)
Ronald Hanson (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - Support TNW, TU Delft - QID/Hanson Lab)
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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.