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 propose a shot-noise limited scheme for characterizing both these kinds of evolutions by employing a modified Mach-Zehnder interferometer. In order to characterize a $N$-mode device, we require $O\left(N^2\right)$ measurements. Although it suffices to use coherent states for the characterization of linear optical systems, we additionally require single photons to characterize quadratically nonlinear optical systems.

• Received 12 July 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052327