Dynamics of Rényi entropy and applications in detecting quantum non-Markovianity

Exploiting the master equations in the Lindblad form, we establish a sufficient and necessary condition for a Markovian dynamics to be unital. Based on this condition, we analyze the dynamical property of quantum Rényi entropy and propose a characterization of quantum non-Markovianity for unital dynamics in terms of Rényi entropy, which contains the previous criteria of non-Markovianity via von Neumann entropy and linear entropy as particular cases. The effectiveness of this measure in capturing the backflow of information from the environment is illustrated through several typical unital dynamics.

Figure 1

Contour plot of the behavior of the derivative about the determinant with respect to time while varying the Ohmicity parameter $s$. When $s\in (2,4)$, the derivative is negative and the dynamics exhibits Rényi non-Markovianity. All quantities are dimensionless.