Direct characterization of Gaussian quantum processes with Gaussian resources*

We develop an efficient procedure to fully characterize arbitrary Gaussian quantum processes in continuous variable quantum systems. This is done by directly obtaining all elements of the symplectic matrix that describes the process. The procedure utilizes a well-characterized coherent probe and employs quadrature detection methods. The procedure involves O(N²) steps to characterize an N-mode Gaussian quantum process. We show how the method naturally simplifies in the case of linear optics. We further demonstrate that the procedure is resilient to loss, and that such loss can be characterized without any modification to our proposed method. We simulate this procedure using the Python package Strawberry Fields, and demonstrate that the reconstruction is accurate