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Quantum observables and effect algebras. (English) Zbl 1394.81020
Summary: We study observables on monotone \(\sigma\)-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone \(\sigma\)-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
46L10 General theory of von Neumann algebras
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