  A central task in quantum information processing is to characterize quantum
processes. In the realm of optical quantum information processing, this amounts
to characterizing the transformations of the mode creation and annihilation
operators. This transformation is unitary for linear optical systems, whereas
these yield the well-known Bogoliubov transformations for systems with
Hamiltonians that are quadratic in the mode operators. In this paper, we show
that a modified Mach-Zehnder interferometer can characterize both these kinds
of evolutions for multimode systems. While it suffices to use coherent states
for the characterization of linear optical systems, we additionally require
single photons to characterize quadratically nonlinear optical systems.
