  This note is concerned with a modified version of the frequency domain
physical realizability (PR) condition for linear quantum systems. We consider
open quantum systems whose dynamic variables satisfy the canonical commutation
relations of an open quantum harmonic oscillator and are governed by linear
quantum stochastic differential equations (QSDEs). In order to correspond to
physical quantum systems, these QSDEs must satisfy PR conditions. We provide a
relatively simple proof that the PR condition is equivalent to the frequency
domain $(J,J)$-unitarity of the input-output transfer function and
orthogonality of the feedthrough matrix of the system without the technical
spectral assumptions required in previous work. We also show that the poles and
transmission zeros associated with the transfer function of PR linear quantum
systems are the mirror reflections of each other about the imaginary axis. An
example is provided to illustrate the results.
