Non-Markovian dynamics of quantum discord

We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.

Figure 1

Analytical ($D_1$, squares; $D_2$, circles) and numerical (solid line) dynamics of discord as a function of the scaled time ${\gamma }_{0}t$ for (a) a common reservoir with $\lambda =0.1{\gamma }_0$ and (b) independent reservoirs with $\lambda =0.01{\gamma }_0$. The dotted lines in (a) indicate the value of ${\gamma }_{0}t$ where the sudden change occurs. The two-qubit initial state used here is given in Eq. (12) with ${\alpha }^2=1/3$.

Figure 2

Dynamics of discord (solid line) and EOF (dashed line) as a function of the scaled time for independent reservoirs with $\lambda =0.01{\gamma }_0$ and the two qubits initially prepared in the state of Eq. (12) with (a) ${\alpha }^2=1/10$, (b) ${\alpha }^2=1/3$, and (c) ${\alpha }^2=1/2$.

Figure 3

Dynamics of discord (solid line) and EOF (dashed line) as a function of the scaled time for common reservoirs with $\lambda =0.1{\gamma }_0$ and two qubits initially prepared in the state of Eq. (12) with (a) ${\alpha }^2=0$, (b) ${\alpha }^2=1/10$, (c) ${\alpha }^2=1/5$, and (d) ${\alpha }^2=1/2$.

Figure 4

Dynamics of discord (solid line) and EOF (dashed line) as a function of the scaled time for a common reservoir with (a) $\lambda =0.1{\gamma }_0$, (b) $\lambda ={\gamma }_0$, and (c) $\lambda =10{\gamma }_0$. The two-qubit initial state is given by Eq. (12) with ${\alpha }^2=1/3$.