Dynamics of quantum coherence in Bell-diagonal states under Markovian channels

We study the curves of coherence for the Bell-diagonal states including $l_{1}$-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under $l_{1}$ norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. We study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem $n$ times and find coherence under depolarizing channel decreases initially then increases for small $n$ and tend to zero for large $n$. We discuss the dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel.Comment: 13 pages, 17 figure

Quantum discord and geometry for a class of two-qubit states

We study the level surfaces of quantum discord for a class of two-qubit states with parallel nonzero Bloch vectors. The dynamic behavior of quantum discord under decoherence is investigated. It is shown that a class of X states has sudden transition between classical and quantum correlations under decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys. Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and structures of quantum discord.Comment: 5 pages, 5 figure