260047 VO Quantum correlations and generalized probabilistic theories: an introduction (2018W)

The goal of this lecture is to provide the theoretical foundations of the operational approach to quantum theory, which is the basis of Quantum Information Theory and the related research field of Quantum Foundations. The main emphasis is on correlations: quantum theory admits “stronger” correlations than classical physics (namely those that violate Bell inequalities), but, surprisingly, even stronger correlations are conceivable (so-called “PR box correlations”). We will first see how such correlations can be described mathematically, and how the violation of Bell inequalities can be used for technological applications (e.g. for the certification of randomness). Then we will see that quantum theory is only a special case of a larger class of generalized probabilistic theories (with physical properties different from quantum theory), and we will derive the Hilbert space formalism (with its operators, complex numbers etc.) from simple physical principles.