  In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered
a general form of master equations for an open quantum Markovian dynamics. In
honor of all the authors, the equation is nowadays called the GKLS master
equation. In this paper, we show universal constraints on the relaxation times
valid for any d-level GKLS master equations, which is a generalization of the
well-known constraints for 2-level systems. Specifically, we show that any
relaxation rate, the inverse-relaxation time, is not greater than half of the
sum of all relaxation rates. Since the relaxation times are measurable in
experiments, our constraints provide a direct experimental test for the
validity of the GKLS master equations, and hence for the conditions of the
complete positivity and Markovianity.
