Structure of Quantum Theory

Any prepare-and-measure experiment involving a single preparation and several possible measurements on this preparation can be conceptualized as a contextuality scenario within the Acín-
Fritz-Leverrier-Sainz (AFLS) framework (Acín et al., Commun. Math. Phys. 334, 533-628 (2015)). Probabilistic models on such contextuality scenarios can describe correlations between measurements in all such experiments. Extremal probabilistic models on a contextuality scenario are those that cannot be understood as convex mixtures of other probabilistic models. We prove a no-go theorem for the quantum realizability of such models: if at least one measurement in a prepare-and-measure experiment with a single preparation is promised to be nontrivial on the preparation, it is impossible to achieve indeterministic extremal probabilistic models (i.e., those with probabilities outside the set {0, 1}). Hence, the only way to “quantumly” achieve such extremal probabilistic models is in experiments where all the measurements are trivial on the preparation, i.e., they can learn nothing about the preparation. To our knowledge, this is the first no-go result for correlations from generically noisy quantum measurements that is applicable to arbitrary contextuality scenarios (and not merely Bell scenarios). We will discuss implications of this no-go theorem for the foundations of quantum theory.