  The aim of quantum system identification is to estimate the ingredients
inside a black box, in which some quantum-mechanical unitary process takes
place, by just looking at its input-output behavior. Here we establish a basic
and general framework for quantum system identification, that allows us to
classify how much knowledge about the quantum system is attainable, in
principle, from a given experimental setup. Prior knowledge on some elements of
the black box helps the system identification. We present an example in which a
Bell measurement is more efficient to identify the system. When the topology of
the system is known, the framework enables us to establish a general criterion
for the estimability of the coupling constants in its Hamiltonian.
