Robust method for estimating the Lindblad operators of a dissipative quantum process from measurements of the density operator at multiple time points

We present a robust method for quantum process tomography, which yields a set of Lindblad operators that optimally fit the density operators measured at a sequence of time points. The benefits of this method are illustrated using a set of liquid-state nuclear magnetic resonance 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.