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Observables on quantum structures. (English) Zbl 1329.81140
Summary: An observable on a quantum structure is any \(\sigma\)-homomorphism of quantum structures from the Borel \({\sigma}\)-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form \((-\infty ,{t})\) is sufficient to derive the whole information about the observable defined on quantum structures like \({\sigma}\)-MV-algebras, \({\sigma}\)-lattice effect algebras, Boolean \({\sigma}\)-algebras, monotone \({\sigma}\)-complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and systems of functions – effect-tribes.

MSC:
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
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