**Quantum process tomography with coherent states**

Assembling a complex quantum optical information processor requires precise knowledge of the properties of each of its components, i.e.,
the ability to predict the effect of the components on an arbitrary input state. This gives rise to a quantum version of the famous â€œblack box
problemâ€, which is addressed by means of â€œquantum process tomographyâ€ (QPT). We develop a new theoretical framework for the general
method of characterizing quantum optical processes [M. Lobino et al., Science 322, 563 (2008)] based on probing the process with coherent
states and using a filtered Glauber-Sudarshan decomposition to determine the effect of the process on an arbitrary state. We introduce a new
method of calculating the process tensor from the known effect of the process on coherent states. This method eliminates the need to filter
the Glauber-Sudarshan representations for states, which significantly simplifies the procedure and permits extension of the method to
multi-mode and non-trace-preserving processes. We illustrate our findings with a set of examples, in which, by knowing the effect of some
of the fundamental quantum optical processes on coherent states, we analytically derive their process tensors in the Fock basis.