  Given any covariance matrix corresponding to a so-called pure Gaussian state,
a linear quantum system can be designed to achieve the assigned covariance
matrix. In most cases, however, one might obtain a system that is difficult to
realize in practice. In this paper, we restrict our attention to a special
class of linear quantum systems, i.e., systems with diagonal passive
Hamiltonian and a single dissipative channel. The practical implementation of
such a system would be relatively simple. We then parametrize the class of pure
Gaussian state covariance matrices that can be achieved by this particular type
of linear quantum system.
