28 research outputs found

    On the Consistent Effect Histories Approach to Quantum Mechanics

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    A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of `history' is generalized to the notion of `effect history'. The space of effect histories carries the structure of a D-poset. Recent results of J.D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnes' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.Comment: LaTeX 2.09 version replaced by LaTeX2e version, minor change

    A representation theorem for MV-algebras

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    An {\em MV-pair} is a pair (B,G)(B,G) where BB is a Boolean algebra and GG is a subgroup of the automorphism group of BB satisfying certain conditions. Let G\sim_G be the equivalence relation on BB naturally associated with GG. We prove that for every MV-pair (B,G)(B,G), the effect algebra B/GB/\sim_G is an MV- effect algebra. Moreover, for every MV-effect algebra MM there is an MV-pair (B,G)(B,G) such that MM is isomorphic to B/GB/\sim_G

    Smearing of Observables and Spectral Measures on Quantum Structures

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    An observable on a quantum structure is any σ\sigma-homomorphism of quantum structures from the Borel σ\sigma-algebra of the real line into the quantum structure which is in our case a monotone σ\sigma-complete effect algebras with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ\sigma-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there is its spectral measure

    Sharp and fuzzy observables on effect algebras

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    Observables on effect algebras and their fuzzy versions obtained by means of confidence measures (Markov kernels) are studied. It is shown that, on effect algebras with the (E)-property, given an observable and a confidence measure, there exists a fuzzy version of the observable. Ordering of observables according to their fuzzy properties is introduced, and some minimality conditions with respect to this ordering are found. Applications of some results of classical theory of experiments are considered.Comment: 23 page

    The Lattice and Simplex Structure of States on Pseudo Effect Algebras

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    We study states, measures, and signed measures on pseudo effect algebras with some kind of the Riesz Decomposition Property, (RDP). We show that the set of all Jordan signed measures is always an Abelian Dedekind complete \ell-group. Therefore, the state space of the pseudo effect algebra with (RDP) is either empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow represent states on pseudo effect algebras by standard integrals

    Ideals and Bosbach States on Residuated Lattices

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