  For quantum systems with linear dynamics in phase space much of classical
feedback control theory applies. However, there are some questions that are
sensible only for the quantum case, such as: given a fixed interaction between
the system and the environment what is the optimal measurement on the
environment for a particular control problem? We show that for a broad class of
optimal (state-based) control problems (the stationary
Linear-Quadratic-Gaussian class), this question is a semi-definite program.
Moreover, the answer also applies to Markovian (current-based) feedback.
