  Quantum speed limits are relations yielding lower bounds on the evolution
time of quantum systems. These results have been generalized in some ways, in
particular by including evolutions to non-orthogonal states. However, there was
a gap in the literature on this area, for only unitary evolutions -- closed
quantum systems -- had been considered. On this Ph.D. thesis, such limitation
is overcome: our main result is a bound for quantum-system evolutions in
general, whether unitary or not, and correctly recovers the known bounds in the
unitary case. Applications of this bound to several concrete cases of interest
are herein presented. This bound is also used to extend to the non-unitary case
the discussion of the role of entanglement in fast evolutions, leading to
nontrivial results.
  For the derivation of the results, a geometric approach has been employed,
which allows a clear interpretation of the bounds and a discussion of the
criteria for their saturation. No previous knowledge of quantum-state geometry
by the reader has been assumed.
