We find the minimal number of settings to test quantum theory based on real numbers, assuming separability of the sources, modifying the recent proposal [M.-O. Renou et al., Nature (London) 600, 625 (2021)]. The test needs only three settings for observers A and C, but the ratio of complex to real maximum is smaller than in the existing proposal. We also found that two settings and two outcomes for both observers are insufficient.
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Bednorz et al. (2022) studied this question.
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