Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality

The characterization of quantum correlations in terms of information-theoretic principles is a popular chapter in quantum foundations. Traditionally, the principles designed for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as "device-independent". Another major topic in quantum foundations is the information-theoretic characterization of quantum theory as a physical theory, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term "general probabilistic theories". With only a few exceptions, the two programmes have proceeded on separate tracks, each one developing its own methods and agenda. However, the two programmes share the same basic goal: a new and better understanding of quantum mechanics in information-theoretic terms. From this viewpoint, it is quite striking that the connections are still largely undeveloped. This paper aims at bridging the gap, by presenting "Rosetta stone" for the two frameworks and by illustrating how ideas from one programme can shed light on the other. As a case study, we focus on two device-independent features known as Local Orthogonality (LO) and Consistent Exclusivity (CE) and reconstruct them from a different set of principles about pure orthogonal measurements, that is, measurements that cannot be further refined and that identifies states without error.