Markovianity of quantum channels and quantum estimation

We investigate how Markovianity of a quantum dynamics may affect accuracy of the estimation of dynamical parameters. For quantum Markovian dynamics, the time derivative of quantum Fisher information (QFI) is shown to be negative. When symmetric logarithmic derivative (SLD) is taken with respect to a parameter of initial state, this negativity demonstrates loss of distinguishability with time. However, when SLD is taken with respect to a dynamical parameter, the negativity of the rate of QFI shows that the state eventually approaches a stationary fixed state. As a result, in this case the estimation of channel parameters becomes difficult with time. [Joint work with A.T. Rezakhani]