Wigner Measures and Quantum Control

This paper considers Wigner functions and measures for infinite-dimensional open quantum systems; important examples of such systems are objects of
quantum control theory. An axiomatic definition of coherent quantum feedback is proposed. A representation of the states of quantum systems in terms of Wigner measures is possible for systems having classical analogues; it is similar to the representation of the states of classical Hamiltonian systems in
terms of probability measures on the phase space. In both cases, the passage to a description of the state of a subsystem of some larger quantum system is implemented by means of the projection operation, because the phase space of the classical analogue of the ambient quantum system, being the union of some subsystems, is the Cartesian product of the phase spaces of the classical analogues of these subsystems.