Four and a Half Axioms for Quantum Mechanics

          @misc{ pirsa_PIRSA:09080015,
            doi = {10.48660/09080015},
            url = {https://pirsa.org/09080015},
            author = {Wilce, Alexander},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Four and a Half Axioms for Quantum Mechanics},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:09080015 see, \url{https://pirsa.org}}
          }
          

Abstract

I will discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. These require that systems appear completely classical as restricted to a single measurement, that different measurements, and likewise different pure states, be equivalent up to the action of a compact group of symmetries, and that every state be the marginal of a bipartite state perfectly correlating two measurements. This much yields a mathematical representation of measurements, states and symmetries that is already very suggestive of quantum mechanics. One final postulate (a simple minimization principle, still in need of a clear interpretation) forces the theory's state space to be that of a formally real Jordan algebra