Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

TL;DR

This paper reports a second loophole-free Bell test using electron spins in diamond, confirming the violation of Bell inequality and strengthening evidence against local realism with robust statistical analysis.

Contribution

It presents a second experimental run with minor modifications, confirming Bell violation and analyzing the robustness against RNG imperfections.

Findings

Bell inequality violation of 2.35 ± 0.18 in the second experiment

Combined Bell test value of 2.38 ± 0.14

Observed settings distributions are consistent with uniform randomness

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 $2.35 \pm 0.18$, in agreement with the first run, yielding an overall value of $S = 2.38 \pm 0.14$. 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, implying that our experimental result is robust for any model underlying the estimated average RNG bias.