We study the entanglement capability of the evolution of a pair of qubits
evolving under unitary dynamics, when the local dynamical parameters cannot be
modified during the time-evolution. Unlike the fast local control regime, we
find that local and non-local contributions to the dynamics are strictly
interconnected. Moreover, it is possible to strongly increase the entanglement
capability by suitably initializing the characteristic energies of the two
parties.Comment: 4 page