文章基本信息

标题：Computability in Basic Quantum Mechanics
本地全文：下载
作者：Streicher, Thomas ; Pape, Martin ; Neumann, Eike 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2018
卷号：14
期号：2
DOI：10.23638/LMCS-14(2:14)2018
语种：English
出版社：Technical University of Braunschweig
摘要：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.
关键词：Computer Science - Logic in Computer Science;03B70; 03F60; 18C50; 68Q55