  System identification is a key enabling component for the implementation of
quantum technologies, including quantum control. In this paper, we consider the
class of passive linear input-output systems, and investigate several basic
questions: (1) which parameters can be identified? (2) Given sufficient
input-output data, how do we reconstruct the system parameters? (3) How can we
optimize the estimation precision by preparing appropriate input states and
performing measurements on the output? We show that minimal systems can be
identified up to a unitary transformation on the modes, and systems satisfying
a Hamiltonian connectivity condition called "infecting" are completely
identifiable. We propose a frequency domain design based on a Fisher
information criterion, for optimizing the estimation precision for coherent
input state. As a consequence of the unitarity of the transfer function, we
show that the Heisenberg limit with respect to the input energy can be achieved
using non-classical input states.
