An effective method of calculating the non-Markovianity $\mathcal{N}$ for single channel open systems

摘要

We propose an effective method which can simplify the optimization of theincrease of the trace distance over all pairs of initial states in calculatingthe non-Markovianity $\mathcal{N}$ for single channel open systems. For theamplitude damping channel, we can unify the results of Breuer $et$ $al$. [Phys.Rev. Lett. \bf 103\rm, 210401 (2009)] in the large-detuning case and theresults of Xu $et$ $al$. [Phys. Rev. A \bf 81\rm, 044105 (2010)] in theresonant case; furthermore, for the general off-resonant cases we can obtain avery tight lower bound of $\mathcal{N}$. As another application of our method, we also discuss $\mathcal{N}$ for thenon-Markovian depolarizing channel.