Non-Markovianity through multipartite correlation measures

We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum, classical, and total correlations can be used to quantify the degree of non-Markovianity of a local quantum decohering process. We illustrate our results by considering the dynamical behavior of the trace-distance correlations in multiqubit systems under local dephasing and generalized amplitude damping.

Figure 1

Illustration of the degree of non-Markovianity $N_F\left(\mathrm{\Phi }\right)$ via locally measured states.

Figure 2

Total correlation as a function of $\tau =({\overline{\gamma }}_A+{\overline{\gamma }}_B)t$ for a two-qubit system under a non-Markovian GAD channel. The initial state is in the $X$ form, with $c_1=0.20, c_2=-0.20, c_3=0.60, c_4=0.50$, and $c_5=0.70$. We have also taken $\epsilon =0.92$ and $\eta =0.5$. The nonmonotonic behavior gets pronounced as we decrease $v$ from the Markovian regime ($v\gg 1$) towards the non-Markovian regime.