  In this paper, we investigate the unified bound of quantum speed limit time
in open systems based on the modified Bures angle. This bound is applied to the
damped Jaynes-Cummings model and the dephasing model, and the analytical
quantum speed limit time is obtained for both models. As an example, the
maximum coherent qubit state with white noise is chosen as the initial states
for the damped Jaynes-Cummings model. It is found that the quantum speed limit
time in both the non-Markovian and the Markovian regimes can be decreased by
the white noise compared with the pure state. In addition, for the dephasing
model, we find that the quantum speed limit time is not only related to the
coherence of initial state and non-Markovianity, but also dependent on the
population of initial excited state.
