Seminar 10. Generalized probability theories

We have talked about what generalized probabilistic theories are. In the most general case, it is reasonable to assume that a set of mixed states can form an arbitrary convex body in some affine space. Over these states, one can define a set of effects. There is a duality between states and effects: a given state can be defined by the action of all possible effects on it; a given effect is defined by the action on all states. If two generalized-probabilistic systems are given, the set of states on the common system can be defined in a non-unique way. At least, it is possible to define the minimal and maximal tensor product, which will not be equal in case both systems are non-classical.