Constraints on relaxation rates for N-level quantum systems

We study the constraints imposed on the population and phase relaxation rates by the requirement that the evolution of the system be completely positive for open N-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit expressions for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, non-trivial constraints on the pure dephasing rates for N>2. The implications of the results are discussed for generic ladder-, Lambda- and V-systems and transitions between degenerate energy levels