We consider how to characterize the dynamics of a quantum system from a
restricted set of initial states and measurements using Bayesian analysis.
Previous work has shown that Hamiltonian systems can be well estimated from
analysis of noisy data. Here we show how to generalize this approach to systems
with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the
process for a range of three-level quantum systems. The results suggest that
the Bayesian estimation of the frequencies and dephasing rates is generally
highly accurate and the main source of errors are errors in the reconstructed
Hamiltonian basis.Comment: 6 pages, 3 figure