  We derive a sharp bound as the quantum speed limit (QSL) for the minimal
evolution time of quantum open systems in the non-Markovian strong-coupling
regime with initial mixed states by considering the effects of both
renormalized Hamiltonian and dissipator. For a non-Markovian quantum open
system, the possible evolution time between two arbitrary states is not unique,
among the set of which we find that the minimal one and its QSL can decrease
more steeply by adjusting the coupling strength of the dissipator, which thus
provides potential improvements of efficiency in many quantum physics and
quantum information areas.
