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There are bipartite quantum nonlocal correlations requiring very lowdetection efficiency to reach the loophole-free regime but that need too manymeasurement settings to be practical for actual experiments. This leads to thegeneral problem of what can be concluded about loophole-free Bell nonlocalityif only a random subset of these settings is tested. Here we develop a methodto address this problem. We show that, in some cases, it is possible to detectloophole-free Bell nonlocality testing only a small random fraction of thesettings. The prize to pay is a higher detection efficiency. The method allowsfor a novel approach to the design of loophole-free Bell tests in which, giventhe dimension of the local system, the visibility, and the detection efficiencyavailable, one can calculate the fraction of the contexts needed to reach thedetection-loophole-free regime. The results also enforce a different way ofthinking about the costs of classically simulating quantum nonlocality, as itshows that the amount of resources that are needed can be made arbitrarilylarge simply by considering more contexts.

Loophole-free Bell tests with randomly chosen subsets of measurement settings