Institute for Quantum Information Seminar
I formulate a system of axioms for a physical theory which are common to both classical and quantum mechanics and incorporate some basic intuition about the laws of physics, such as the existence of composite systems and the relation between symmetries and conservation laws. I prove that if systems with finite-dimensional spaces of observables exist, then Quantum Mechanics is the only possible theory of this sort. Even if some of the axioms are dropped, one can show that Quantum Mechanics cannot be deformed by a small parameter. These results show that the laws of Quantum Mechanics are exact, unless some deeply cherished assumptions about the structure of physical laws are wrong.