Seminar 11. Properties of maps in generalized probability theories

We have talked about different channels in generalized probabilistic theories: state preparations, state preparations depending on classical input, discarding and partial trace channels, entanglement-breaking channels, measurements – and dual channels to them. In the field of generalized probabilistic theories, one can study the phenomena of cohesion of different channels – on the one hand, this is a generalization of the idea of studying compatible measurements, and on the other hand is related to the broadcasting operation. Any entanglement-breaking operations are compatible with any other channels, while the identity mapping operation on a quantum system is only compatible with the discarding channel. Also, we talked a bit about a generalized probabilistic theory describing the behavior of players in nonlocal games – in such a theory we can interpret Popescu-Rohrlich boxes.