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Center for Nonlinear Studies |
What is the physical principle that singles out the quantum correlations for Bell and contextuality scenarios? Here we review an unconventional approach to address this question. We show that, if we restrict our attention to correlations that, as is the case for all correlations in classical and quantum physics, can be produced by measurements that (i) yield the same outcome when repeated, (ii) only disturb measurements that are not jointly measurable, and (iii) all their coarse-grainings have realizations that satisfy (i) and (ii), then the question has a surprising answer. The set of quantum correlations is singled out by the following principle: no law restricts the outcomes of the measurements; every outcome probability distribution that is not inconsistent does take place. "Not inconsistent'" distributions are defined through a necessary condition based on the observation that, for measurements satisfying (iii), the sum of the probabilities of any set of pairwise exclusive events is bounded by one. Two events are exclusive when they are produced by the same measurement and each of them correspond to a different outcome. The unconventional character of the approach comes from the fact that, to prove the result, we begin treating all Bell and contextuality scenarios at once and characterize the sets of not inconsistent probability distribution for each "graph of exclusivity," without referring to any particular scenario. The restrictions of each scenario are introduced at the end of the proof and then we obtain the set of probability distributions that satisfies the above principle for each scenario. Each of these sets is equal to the corresponding set in quantum theory.
Host: Lukasz Cincio