Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics

Abstract

I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations between, probabilistic models. The key tool is the Koecher-Vinberg Theorem, which identifies formally real Jordan algebras with finite-dimensional order-unit spaces having homogeneous, self-dual cones.

References in corpus (3)

• Reformulating and Reconstructing Quantum Theory
• Cloning and Broadcasting in Generic Probabilistic Theories
• On quantum vs. classical probability

Cited by in corpus (5)

• Conjugates, Filters and Quantum Mechanics
• Symmetry and Self-Duality in Categories of Probabilistic Models
• A Royal Road to Quantum Theory (or Thereabouts), Extended Abstract
• Paradoxical consequences of multipath coherence: perfect interaction-free measurements
• Local tomography and the Jordan structure of quantum theory