  Consider a quantum system prepared in an input state. One wants to drive it
into a target state. Assuming classical states and operations as free
resources, I identify a geometric cost function which quantifies the difficulty
of the protocol in terms of how different it is from a classical process. The
quantity determines a lower bound to the number of commuting unitary
transformations required to complete the task. I then discuss the link between
the quantum character of a state preparation and the amount of coherence and
quantum correlations that are created in the target state.
