  Quantum process tomography --- a primitive in many quantum information
processing tasks --- can be cast within the framework of the theory of design
of experiment (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 cannot, however,
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.
