Macroscopic noncontextuality as a principle for almost-quantum correlations

Quantum mechanics allows only certain sets of experimental results (or “probabilistic models”) for Bell-type quantum nonlocality 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 Acín, 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 noncontextuality 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 characterization of the almost-quantum set from a simple physical principle.

Figure 1

Microscopic experiment. A source S prepares a system $s$, which is sent to the measurement device M. There, an interaction between the measurement apparatus and the system sends the system towards one of a set of detectors, where its presence can be observed as a “detector click.” The clicking of detector ${\mathrm{D}}_k$ corresponds to obtaining outcome $k$.

Figure 2

Macroscopic experiment. A source S prepares $N$ independent copies of a system $s$, which are sent to the measurement device M. There, for each system (and independently for each system), an interaction between the measurement apparatus and the system sends the system towards one of a set of detectors. However, in this case, rather than a single click, there is a distribution of “clicks” over the detectors according to the probabilities for each outcome in the microscopic experiment. Hence, the “output” of this macroscopic experiment is the collection of intensities $I_e^v$ registered at the detectors.

Figure 3

Construction of the CHSH scenario $B_{2,2,2}$. This figure is originally Fig. 7 in [19].