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

TL;DR

This paper introduces a simplified and effective method for calculating the non-Markovianity measure in single channel open quantum systems, unifying previous results and providing tight bounds for various cases.

Contribution

The paper presents a new method that simplifies the optimization process in calculating non-Markovianity, unifies existing results, and extends analysis to off-resonant and depolarizing channels.

Findings

Unified results for amplitude damping channels in different regimes.

Derived tight lower bounds for non-Markovianity in off-resonant cases.

Applied the method to non-Markovian depolarizing channels.

Abstract

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 $\mathcal{N}$ for single channel open systems. For the amplitude 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 the results of Xu $et$ $al$. [Phys. Rev. A \bf 81\rm, 044105 (2010)] in the resonant case; furthermore, for the general off-resonant cases we can obtain a very tight lower bound of $\mathcal{N}$. As another application of our method, we also discuss $\mathcal{N}$ for the non-Markovian depolarizing channel.