**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 “black box problem”, which is addressed by means of “quantum process tomography” (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.