- Entropy (Entropy) Journal
- November 2020
- 11, 1292
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 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.
- quantum mechanics; entanglement; schwinger's selective measurements; composite systems; groupoids picture of quantum mechanics; groupoids; birkhoff-von neumann logic; foundations of quantum theories