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- W2963705878 abstract "The basic notions of quantum mechanics are formulated in terms of separableinfinite dimensional Hilbert space $mathcal{H}$. In terms of the Hilbertlattice $mathcal{L}$ of closed linear subspaces of $mathcal{H}$ the notionsof state and observable can be formulated as kinds of measures as in [21]. Theaim of this paper is to show that there is a good notion of computability forthese data structures in the sense of Weihrauch's Type Two Effectivity (TTE)[26]. Instead of explicitly exhibiting admissible representations for the datatypes under consideration we show that they do live within the category$mathbf{QCB}_0$ which is equivalent to the category $mathbf{AdmRep}$ ofadmissible representations and continuously realizable maps between them. Forthis purpose in case of observables we have to replace measures by valuationswhich allows us to prove an effective version of von Neumann's SpectralTheorem." @default.
- W2963705878 created "2019-07-30" @default.
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- W2963705878 date "2016-10-27" @default.
- W2963705878 modified "2023-09-24" @default.
- W2963705878 title "Computability in Basic Quantum Mechanics" @default.
- W2963705878 hasPublicationYear "2016" @default.
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