A geometric approach to quantum control in a classical-like framework

A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by Hilbert projective space. This paper is devoted to investigate how the notion of accessibility algebra from classical control theory can be applied within geometric classical-like formulation of Quanum Mechanics to study controllability of a quantum system in order to state the following conjecture: Under certain conditions, classical control theory provides a machinery which can be directly applied in quantum control within the geometric Hamiltonian picture.