  We present a systems theory approach to the proof of a result bounding the
required level of added quantum noise in a phase-insensitive quantum amplifier.
We also present a synthesis procedure for constructing a quantum optical
phase-insensitive quantum amplifier which adds the minimum level of quantum
noise and achieves a required gain and bandwidth. This synthesis procedure is
based on a singularly perturbed quantum system and leads to an amplifier
involving two squeezers and two beamsplitters.
