  The concept of quantum speed limit-time (QSL) was initially introduced as a
lower bound to the time interval that a given initial state $\psi_I$ may need
so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S.
Lloyd, and L. Maccone, Phys. Rev. A {\bf 67}, 052109 (2003)] this bound has
been generalized to the case where $\psi_I$ does not necessarily evolve into an
orthogonal state, but into any other $\psi_F$. It was pointed out that, for
certain classes of states, quantum entanglement enhances the evolution "speed"
of composite quantum systems. In this work we provide an exhaustive and
systematic QSL study for pure and mixed states belonging to the whole
15-dimensional space of two qubits, with $\psi_F$ a not necessarily orthogonal
state to $\psi_I$. We display convincing evidence for a clear correlation
between concurrence, on the one hand, and the speed of quantum evolution
determined by the action of a rather general local Hamiltonian, on the other
one.
