Our result derives from this concept of macroscopic observables being a kind of average. There is a limit to the number of quantum correlations each particle can have with another, which is referred to as the “monogamy” of quantum correlations. The concept is simple: if particles A and B exhibit correlations of the kind predicted in the EPR experiment then A and B can only have local and realistic correlations with other particles...
This monogamous behaviour extends to correlations between larger groups of quantum particles, which is the main idea behind our result. Imagine you are making a macroscopic measurement between two regions in space, A, containing quantum particles A1, A2, A3, etc., and B, containing B1, B2, B3, etc. The measurement samples all possible pairs. Due to monogamy, as you increase the number of particles, the overall strength of the correlations measured dilutes. For instance, AiBj may be strongly correlated but then Ai and any other B-particle exhibit only local realistic correlations (see figure). Analysing the statistics, we find that local realism emerges for macroscopic correlations without us needing to invoke any other mechanism.
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