Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements

Abstract

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.

6 pages, 1 figure

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• Operational restrictions in general probabilistic theories
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• Proposed experiment to test fundamentally binary theories
• Measurement-device-independent quantification of irreducible high-dimensional entanglement
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• Generalised Kochen-Specker Theorem for Finite Non-Deterministic Outcome Assignments
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• Reliable optimization of arbitrary functions over quantum measurements