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We show that, for any n, there are m-outcome quantum correlations, with m>n, which are stronger than any nonsignaling correlation produced from selecting among n-outcome measurements. As a consequence, for any n, there are m-outcome quantum measurements that cannot be constructed by selecting locally from the set of n-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most n-outcome quantum measurements.
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations t
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It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of relativistic ca
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