  The purpose of this paper is to study the structure of quantum linear systems
in terms of their Kalman canonical form, which was proposed in a recent paper
\cite{ZGPG18}. The spectral structure of quantum linear systems is explored,
which indicates that a quantum linear system is both controllable and
observable provided that it is Hurwitz stable. A new parameterization method
for quantum linear systems is proposed. This parameterization is designed for
the Kalman canonical form directly. Consequently, the parameters involved are
in a blockwise form in correspondence with the blockwise structure of the
Kalman canonical form. This parameter structure can be used to simplify various
quantum control design problems. For example, necessary and sufficient
conditions for the realization of quantum back-action evading (BAE)
measurements are given in terms of these new parameters. Due to their blockwise
nature, a small number of parameters are required for realizing quantum BAE
measurements.
