On Ideal Measurements and Their Corresponding Instruments on von Neumann Algebras |
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Authors: | ?uczak Andrzej |
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Affiliation: | (1) Faculty of Mathematics, ód , University ul, Stefana Banacha 22, 90-238 ód , Poland |
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Abstract: | We study some features of quantum measurement in the framework of the theory of instruments — a mathematical model for measurement theory. This investigation is carried in an algebraic formalism in which the observables are represented by elements of a von Neumann algebra and the states are linear normal positive functionals on this algebra. We give a characterization of ideal instruments and study their connections with weakly and strongly repeatable instruments under the assumption that the associated observables are projection-valued measures. We also show that the observables of ideal weakly repeatable instruments must be projection-valued measures. |
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