  Physical Realizability addresses the question of whether it is possible to
implement a given linear time invariant (LTI) system as a quantum system. A
given synthesized quantum controller described by a set of stochastic
differential equations does not necessarily correspond to a physically
meaningful quantum system. However, if additional quantum noises are permitted
in the implementation, it is always possible to implement an arbitrary LTI
system as a quantum system. In this paper, we give an expression for the number
of introduced noise channels required to implement a given LTI system as a
quantum system. We then consider the special case where only the transfer
function to be implemented is of interest. We give results showing when it is
possible to implement a transfer function as a quantum system by introducing
the same number of quantum noises as there are system outputs. Finally, we
demonstrate the utility of these results by providing an algorithm for
obtaining a suboptimal solution to a coherent quantum LQG control problem.
