  Physical Realizability addresses the question of whether it is possible to
implement a given LTI system as a quantum system. It is in general not true
that a given synthesized quantum controller described by a set of stochastic
differential equations is equivalent to some 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 exact number of
noises required to implement a given LTI system as a quantum system.
Furthermore, we focus our attention on proving that this is a minimum, that is,
it is not possible to implement the system as a quantum system with a smaller
number of additional quantum noises.
