A unified bound on the quantum speed limit is obtained for open quantum systems with a mixed initial state by utilizing the function of relative purity proposed by F. Campaioli et al. [Phys. Rev. Lett. 120, 060409 (2018)]. As applications, it is found that the quantum speed limit bound for the damped Jaynes-Cummings model is determined by the competition among the non-Markovianity, the population of the initial excited state, and the initial-state coherence, which shows that the population of the initial excited state and the coherence of the initial state can make the quantum speed limit bound tighter even though the non-Markovian effects can accelerate the evolution of open quantum system. For the dephasing model, a simple factorization law with the initial-state coherence shows that the quantum speed limit is governed by only the competition between the non-Markovianity and the coherence of the initial state.

• Received 24 June 2018

DOI:https://doi.org/10.1103/PhysRevA.98.042132