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.
Highlights
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
In 1964, John Bell found that the correlations between outcomes of distant measurements allowed under local realism1 are strictly bounded, while certain quantum mechanical states are predicted to violate this bound2
Last year we reported the first experimental loophole-free violation of the CHSH-Bell inequality using entangled electron spins associated with nitrogen-vacancy (NV) centers in diamond, separated by 1.3 km17
Summary
After finishing the first loophole-free Bell experiment in July 2015, both the A(lice) and B(ob) setups were modified and used in various local experiments. After each potential heralding event (corresponding to the E-events described in the Supplementary Information of Hensen et al.17), both at location A and B we take 8 new bits from a predefined random dataset (one for A and one for B) based on Twitter messages, to send to the FPGA-based random-number combiner (see Fig. 1). We expand the statistical analysis used for the first run to incorporate the ψ− and ψ+ events into one hypothesis test For each of these states we perform a different variant of the CHSH game, and use the methods of Elkouss and Wehner to combine the two: The output signal of the “event-ready”-box tm = (ti)im=1 has three possible outcomes, where the tag ti = 0 still corresponds to a failure (no, not ready) event.
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