Evolution of classical and quantum states in the groupoid picture of quantum mechanics Articles uri icon

publication date

  • November 2020

start page

  • 1

end page

  • 18


  • 11, 1292


  • 22

International Standard Serial Number (ISSN)

  • 1099-4300


  • 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.


  • Mathematics
  • Physics


  • quantum mechanics; entanglement; schwinger's selective measurements; composite systems; groupoids picture of quantum mechanics; groupoids; birkhoff-von neumann logic; foundations of quantum theories