  This paper extends previous results on constructing a direct coupling quantum
observer for a quantum harmonic oscillator system. In this case, we consider a
complex linear quantum system plant consisting of a network of quantum harmonic
oscillators. Conditions are given for which there exists a direct coupling
observer which estimates a collection of variables in the quantum plant. It is
shown that the order of the observer can be the same as the number of variables
to be estimated when this number is even and thus this is a reduced order
observer.
