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For quantum systems with linear dynamics in phase space much of classicalfeedback control theory applies. However, there are some questions that aresensible only for the quantum case, such as: given a fixed interaction betweenthe system and the environment what is the optimal measurement on theenvironment for a particular control problem? We show that for a broad class ofoptimal (state-based) control problems (the stationaryLinear-Quadratic-Gaussian class), this question is a semi-definite program.Moreover, the answer also applies to Markovian (current-based) feedback.Comment: 5 pages. Version published by Phys. Rev. Let

Optimal Unravellings for Feedback Control in Linear Quantum Systems