Symmetry, SelfDuality and the Jordan Structure of Quantum Theory Speaker(s): Alexander Wilce
Abstract: This talk reviews recent and ongoing work, much of it joint with Howard Barnum, on the origins of the Jordanalgebraic structure of finitedimensional quantum theory. I begin by describing a simple recipe for constructing highly symmetrical probabilistic models, and discuss the ordered linear spaces generated by such models. I then consider the situation of a probabilistic theory consisting of a symmetric monoidal *category of finitedimensional such models: in this context, the state and effect cones are selfdual. Subject to a further ``steering" axiom, they are also homogenous, and hence, by the KoecherVinberg Theorem, representable as the cones of formally real Jordan algebras. Finally, if the theory contains a single system with the structure of a qubit, then (by a result of H. HancheOlsen), each model in the category is the selfadjoint part of a C*algebra.
Date: 10/05/2011  11:40 am
