Quantum process tomography via optimal design of experiments

Quantum process tomography, a primitive in many quantum information processing tasks, can be cast within the framework of the theory of design of experiments (DOE), a branch of classical statistics that deals with the relationship between inputs and outputs of an experimental setup. Such a link potentially gives access to the many ideas of the rich subject of classical DOE for use in quantum problems. The classical techniques from DOE, however, cannot be directly applied to the quantum process tomography due to the basic structural differences between the classical and quantum estimation problems. Here we properly formulate quantum process tomography as a DOE problem and examine several examples to illustrate the link and the methods. In particular, we discuss the common issue of nuisance parameters and point out interesting features in the quantum problem absent in the usual classical setting.