Macroscopic non-contextuality as a principle for Almost Quantum Correlations

Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type quantum non-locality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. "Macroscopic locality," which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models. A similar question can also be asked about probabilistic models for the more general class of quantum contextuality experiments. Here, we extend the Macroscopic Locality principle to this more general setting, using the hypergraph approach of Ac\'in, Fritz, Leverrier and Sainz [Comm. Math. Phys. 334(2), 533-628 (2015)], which provides a framework to study both phenomena of nonlocality and contextuality in a unified manner. We find that the set of probabilistic models allowed by our Macroscopic Non-Contextuality principle is equivalent to an important and previously studied set in this formalism, which is slightly larger than the quantum set. In the particular case of Bell Scenarios, this set is equivalent to the set of "Almost Quantum" models, which is of particular interest since the latter was recently shown to satisfy all but one of the principles that have been proposed to bound quantum probabilistic models, without being implied by any of them (or even their conjunction). Our condition is the first characterisation of the almost quantum set from a simple physical principle.