260022 VU Probabilistic theories and reconstructions of quantum theory (2023W)

Quantum theory is one of our most successful physical theories, but its standard textbook formulation is quite mysterious. For example, why are states described by complex vectors in a Hilbert space, and why do observables correspond to self-adjoint operator? In this lecture, we will see how the formalism of quantum theory can be derived from simple physical or information-theoretic principles. This is similar to the derivation of the Lorentz transformations from the relativity principle and the constancy of the speed of light. To this end, we will study the framework of “generalized probabilistic theories”, which generalizes both classical and quantum probability theory and which has become an indispensable tool in quantum information theory research over the last few years. Students will also gain knowledge of important aspects of convex geometry, duality, and group representation theory which are very useful in other areas of theoretical physics, in particular in quantum information theory.