  The purpose of this paper is to investigate system identification for
single-input-single-output general (active or passive) quantum linear systems.
For a given input we address the following questions: (1) Which parameters can
be identified by measuring the output? (2) How can we construct a system
realization from sufficient input-output data? We show that for time-dependent
inputs, the systems which cannot be distinguished are related by symplectic
transformations acting on the space of system modes. This complements a
previous result for passive linear systems. In the regime of stationary quantum
noise input, the output is completely determined by the power spectrum. We
define the notion of global minimality for a given power spectrum, and
characterize globally minimal systems as those with a fully mixed stationary
state. We show that in the case of systems with a cascade realization, the
power spectrum completely fixes the transfer function, so the system can be
identified up to a symplectic transformation. We give a method for constructing
a globally minimal subsystem direct from the power spectrum. Restricting to
passive systems the analysis simplifies so that identifiability may be
completely understood from the eigenvalues of a particular system matrix.
