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

TL;DR

This paper introduces a method to perform loophole-free Bell tests using only a random subset of measurement settings, reducing experimental complexity at the cost of higher detection efficiency.

Contribution

It develops a novel approach to Bell tests that requires testing only a small random fraction of settings, enabling more practical loophole-free experiments.

Findings

Loophole-free Bell nonlocality can be detected with a small random subset of settings.

Higher detection efficiency is necessary when using fewer measurement settings.

The method allows calculating the minimal fraction of settings needed based on system parameters.

Abstract

There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general problem of what can be concluded about loophole-free Bell nonlocality if only a random subset of these settings is tested. Here we develop a method to address this problem. We show that, in some cases, it is possible to detect loophole-free Bell nonlocality testing only a small random fraction of the settings. The prize to pay is a higher detection efficiency. The method allows for a novel approach to the design of loophole-free Bell tests in which, given the dimension of the local system, the visibility, and the detection efficiency available, one can calculate the fraction of the contexts needed to reach the detection-loophole-free regime. The results also enforce a different way of thinking about the costs of classically simulating quantum nonlocality, as it shows that the amount of resources that are needed can be made arbitrarily large simply by considering more contexts.