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Keywords = Schwinger’s selective measurements

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18 pages, 329 KB  
Article
Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics
by Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort and Giuseppe Marmo
Entropy 2020, 22(11), 1292; https://doi.org/10.3390/e22111292 - 13 Nov 2020
Cited by 8 | Viewed by 2412
Abstract
The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, [...] Read more.
The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations)
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