Optimal experiment design for quantum state tomography of a molecular vibrational mode

Optimal experiment design is used to collect a data set for the complete reconstruction of the vibrational quantum state of diatomic potassium molecules with maximum accuracy and a minimum number of experiments. The optimal configuration of experimental settings is obtained by minimizing the Cramér-Rao lower bound to the accuracy, which is attained in our reconstruction. The quantum state is reconstructed from the data set using maximum-likelihood estimation. Both optimal experiment design and maximum-likelihood estimation are solved efficiently as convex optimization problems.