Effective method of calculating the non-Markovianity N for single-channel open systems

We propose an effective method which can simplify the optimization of the increase of the trace distance over all pairs of initial states in calculating the non-Markovianity N for single-channel open systems. For the amplitude-damping channel, we can unify the results of Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009)] in the large-detuning case and the results of Xu et al. [Phys. Rev. A 81, 044105 (2010)] in the resonant case; furthermore, for the general off-resonant cases, we can obtain a very tight lower bound of N. As another application of our method, we also discuss N for the non-Markovian depolarizing channel.