  We describe an approach for characterizing the process of quantum gates using
quantum process tomography, by first modeling them in an extended Hilbert
space, which includes non-qubit degrees of freedom. To prevent unphysical
processes from being predicted, present quantum process tomography procedures
incorporate mathematical constraints, which make no assumptions as to the
actual physical nature of the system being described. By contrast, the
procedure presented here ensures physicality by placing physical constraints on
the nature of quantum processes. This allows quantum process tomography to be
performed using a smaller experimental data set, and produces parameters with a
direct physical interpretation. The approach is demonstrated by example of
mode-matching in an all-optical controlled-NOT gate. The techniques described
are non-specific and could be applied to other optical circuits or quantum
computing architectures.
