文章基本信息

标题：A Diagrammatic Approach to Quantum Dynamics
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作者：Stefano Gogioso
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：139
页码：1-23
DOI：10.4230/LIPIcs.CALCO.2019.19
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We present a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables. We provide physical semantics to our approach in terms of quantum clocks and quantisation of time. We show that quantum dynamical systems arise naturally as the algebras of a certain dagger Frobenius monad, with the morphisms and tensor product of the category of algebras playing the role, respectively, of equivariant transformations and synchronised parallel composition of dynamical systems. We show that the Weyl Canonical Commutation Relations between time and energy are an incarnation of the bialgebra law and we derive SchrÃ¶dinger's equation from a process-theoretic perspective. Finally, we use diagrammatic symmetry-observable duality to prove Stone's proposition and von Neumann's Mean Ergodic proposition, recasting the results as two faces of the very same coin.
关键词：Quantum dynamics; String diagrams; Categorical algebra