  We present a robust method for quantum process tomography, which yields a set
of Lindblad operators that optimally fit the measured density operators at a
sequence of time points. The benefits of this method are illustrated using a
set of liquid-state Nuclear Magnetic Resonance (NMR) measurements on a molecule
containing two coupled hydrogen nuclei, which are sufficient to fully determine
its relaxation superoperator. It was found that the complete positivity
constraint, which is necessary for the existence of the Lindblad operators, was
also essential for obtaining a robust fit to the measurements. The general
approach taken here promises to be broadly useful in studying dissipative
quantum processes in many of the diverse experimental systems currently being
developed for quantum information processing purposes.
