An operational, convex-geometric framework that generalizes classical probability by dropping the assumption that all measurements can be performed jointly, recovering classical and quantum theory as special cases and admitting hypothetical post-quantum theories. Students learn to model a physical system by its state space and effect space as ordered vector spaces and cones, to represent measurements and composite systems using tensor products, and to see non-classical features such as entanglement as generic properties of these theories rather than uniquely quantum ones.
Lecture notes from a short course (Perimeter Institute, 2024) giving a unified, historically-informed introduction to generalized probabilistic theories (GPTs). GPTs generalize classical probability …