Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control

Arbitrary linear time invariant systems can be implemented as quantum systems if additional quantum noises are permitted in the implementation. We give several results concerning how many additional quantum noise channels are necessary to implement state space realizations and transfer functions as quantum systems. We also give algorithms to do so. We demonstrate the utility of these results with an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.