  This paper proposes a direct coupling coherent quantum observer for a quantum
plant which consists of a two level quantum system. The quantum observer, which
is a quantum harmonic oscillator, includes homodyne detection measurements. It
is shown that the observer can be designed so that it does not affect the
quantum variable of interest in the quantum plant and that measured output
converges in a given sense to the plant variable of interest. Also, the plant
variable of interest-observer system can be described by a set of linear
quantum stochastic differential equations. A minimum variance unbiased
estimator form of the Kalman filter is derived for linear quantum systems and
applied to the direct coupled coherent quantum observer.
