  We introduce the concept of Magic Subspaces for the control of dissipative N-
level quantum systems whose dynamics are governed by Lindblad equation. For a
given purity, these subspaces can be defined as the set of density matrices for
which the rate of purity change is maximum or minimum. Adding fictitious
control fields to the system so that two density operators with the same purity
can be connected in a very short time, we show that magic subspaces allow to
derive a purity speed limit, which only depends on the relaxation rates. We
emphasize the superiority of this limit with respect to established bounds and
its tightness in the case of a two-level dissipative quantum system. The link
between the speed limit and the corresponding time-optimal solution is
discussed in the framework of this study. Explicit examples are described for
two- and three- level quantum systems.
