Dynamics of cohering and decohering power under Markovian channels

Abstract: In this paper, we investigate the cohering and decohering power for the one-qubit Markovian channels with respect to coherence in terms of the $l_{1}$-norm, the R$\acute{e}$nyi $\alpha$-relative entropy and the Tsallis $\alpha$-relative entropy. In the case of $\alpha=2$, the cohering and decohering power of the amplitude damping channel, the phase damping channel, the depolarizing channel, and the flip channels under the three measures of coherence are calculated analytically. The decohering power on the $x, y, z$ basis referring to the amplitude damping channel, the phase damping channel, the flip channel for every measure we investigated is equal. This property also happens in the cohering power of the phase damping channel, the depolarizing channel, and the flip channels. However, the decohering power of the depolarizing channel is independent to the reference basis, and the cohering power of the amplitude damping channel on the $x, y$ basis is different to that on the $z$ basis.