Coherent quantum observers for n-level quantum systems

The purpose of this paper is to find coherent quantum observers for open n-level quantum systems. Recently, a class of linear coherent observers has been developed for quantum harmonic oscillators. However, open n-level quantum systems, which are characterized by bilinear quantum stochastic differential equations, escape the realm of the known theory. Therefore, in this paper we show how a coherent quantum observer is designed to track the corresponding n-level quantum plant asymptotically in the sense of mean values. We also discuss suboptimal quantum observers in the sense of least mean squares estimation.