AA 2021-222, Alessandro Toigo

1. Basic formalism:
   • von Neumann algebras;
   • states and observables;
   • composite systems;
   • omplete positivity and channels;
   • dilation theorems and purifications.
2. Three applications:
   • the Schrödinger-HJW theorem;
   • Fidelity and Uhlmann’s theorem;
   • reversible channels.
3. Impossible devices and incompatible channels:
   • joint measurements;
   • cloning;
   • measuring without disturbance;
   • classical teleportation;
   • Bell telephone.
4. Possible devices and uncertainty relations:
   • preparation and measurement uncertainty relations;
   • noise-disturbance relations;
   • approximate cloning.