  The paper is concerned with a problem of coherent (measurement-free)
filtering for physically realizable (PR) linear quantum plants. The state
variables of such systems satisfy canonical commutation relations and are
governed by linear quantum stochastic differential equations, dynamically
equivalent to those of an open quantum harmonic oscillator. The problem is to
design another PR quantum system, connected unilaterally to the output of the
plant and playing the role of a quantum filter, so as to minimize a mean square
discrepancy between the dynamic variables of the plant and the output of the
filter. This coherent quantum filtering (CQF) formulation is a simplified
feedback-free version of the coherent quantum LQG control problem which remains
open despite recent studies. The CQF problem is transformed into a constrained
covariance control problem which is treated by using the Frechet
differentiation of an appropriate Lagrange function with respect to the
matrices of the filter.
