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Characterizing quantum correlations in terms of information-theoreticprinciples is a popular chapter of quantum foundations. Traditionally, theprinciples adopted for this scope have been expressed in terms of conditionalprobability distributions, specifying the probability that a black box producesa certain output upon receiving a certain input. This framework is known as"device-independent". Another major chapter of quantum foundations is theinformation-theoretic characterization of quantum theory, with its sets ofstates and measurements, and with its allowed dynamics. The differentframeworks adopted for this scope are known under the umbrella term "generalprobabilistic theories". With only a few exceptions, the two programmes oncharacterizing quantum correlations and characterizing quantum theory have sofar proceeded on separate tracks, each one developing its own methods and itsown agenda. This paper aims at bridging the gap, by comparing the twoframeworks and illustrating how the two programmes can benefit each other.

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