Typical Local Measurements in Generalized Probabilistic Theories: Emergence of Quantum Bipartite Correlations

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

Figure 1

Typical two-dimensional sections of a hypercube and of the effect space of a PR box in various dimensions. In both cases an increasing rounding of the corners of the sections can be observed. However in the case of a hypercube, which is the extremal situation for Dvoretzky’s theorem, there is still an appreciable probability for nonrounded sections, due to low dimensionality.