  Determining the Markovianity and non-Markovianity of a quantum process is a
critical problem in the theory of open quantum systems, as their behaviors
differ significantly in terms of complexity. It is well recognized that a
quantum process is Markovian if and only if the quantum master equation can be
written in the standard Lindblad form with all rates nonnegative for all time.
However, here we present a striking result that \textit{any} finite-dimensional
open quantum system dynamics can be described by a quantum master equation in
the Lindblad form with all rates nonnegative for all time. In fact, it can be
shown that one can arbitrarily decide the sign of the rates in any case at any
time interval. Note that here we take an unconventional approach where the
quantum master equation we construct will in general be state-dependent, which
means that the Hamiltonian, jump operators and rates will all depend on the
current state of the density matrix $\rho(t)$. Our findings raise serious
questions on the current criterion in determining Markovianity and
non-Markovianity in open quantum system dynamics.
