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

Signs of the rates in the Lindblad master equations can always be arbitrarily determined