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We consider how to characterize the dynamics of a quantum system from arestricted set of initial states and measurements using Bayesian analysis.Previous work has shown that Hamiltonian systems can be well estimated fromanalysis of noisy data. Here we show how to generalize this approach to systemswith moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate theprocess for a range of three-level quantum systems. The results suggest thatthe Bayesian estimation of the frequencies and dephasing rates is generallyhighly accurate and the main source of errors are errors in the reconstructedHamiltonian basis.

Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography