Symmetry and Self-Duality in Categories of Probabilistic Models
arXiv:1210.0622 · doi:10.4204/EPTCS.95.19
Abstract
This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic structure of finite-dimensional quantum theory. The derivation relies on the Koecher-Vinberg Theorem, which sets up an equivalence between order-unit spaces having homogeneous, self-dual cones, and formally real Jordan algebras.
arXiv commentIn Proceedings QPL 2011, arXiv:1210.0298
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- Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories