  A quantum theory in a finite-dimensional Hilbert space can be geometrically
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 projective Hilbert space. This paper is devoted to
investigate how the notion of accessibility algebra from classical control
theory can be applied within geometric Hamiltonian formulation of Quanum
Mechanics to study controllability of a quantum system. A new characterization
of quantum controllability in terms of Killing vector fields w.r.t.
Fubini-Study metric on projective space is also discussed.
