  We consider a coherent-classical estimation scheme for a class of linear
quantum systems. It comprises an estimator that is a mixed quantum-classical
system without involving coherent feedback. The estimator yields a classical
estimate of a variable for the quantum plant. We demonstrate that for a passive
plant that can be characterized by annihilation operators only, such
coherent-classical estimation provides no improvement over purely-classical
estimation. An example is also given which shows that if the plant is not
assumed to be an annihilation operator only quantum system, it is possible to
get better estimates with such coherent-classical estimation compared with
purely-classical estimation.
