Analytical results for coherent state quantum process tomography

A general method of characterizing quantum optical process was introduced in [1], based on probing with coherent states and approximating the P-function with a regular function. In the present work, by considering the fact that in a realistic experiment we are dealing with a finite dimensional Hilbert space, the approximation for P-function can be avoided. We extend the technique to the multimode case and to conditional processes. Furthermore, based on the effect of some of the fundamental quantum optical processes on the coherent states, we analytically derive their superoperator in the Fock basis.