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Physical Realizability addresses the question of whether it is possible toimplement a given LTI system as a quantum system. It is in general not truethat a given synthesized quantum controller described by a set of stochasticdifferential equations is equivalent to some physically meaningful quantumsystem. However, if additional quantum noises are permitted in theimplementation it is always possible to implement an arbitrary LTI system as aquantum system. In this paper we give an expression for the exact number ofnoises 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 smallernumber of additional quantum noises.

Quantum Implemention of an LTI System with the minimal number of additional quantum noise inputs