Quantum Mechanics as Quantum Probability

Quantum mechanics is naturally to be seen as a probability theory for the description of statistical experiments, also valid at a microscopic level. To highlight this fact, we first address the general formulation of a statistical theory, which is relevant for the description of physical systems in which the outcomes of an experiment have to be described by a probability distribution. We briefly outline the frameworks corresponding to a classical and a quantum formulation, starting to analyze the distinguishing features of the latter.