An Optimization Problem from Linear Filtering with Quantum Measurements

J.S. Baras

Journal of Applied Mathematics and Optimization,Vol. 18, pp. 191-214, 1988

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Abstract

We consider the problem of optimal (in the sense of minimum error variance) linear filtering a vector discrete-time signal process, which
influences a quantum mechanical field, utilizing quantum mechanical measurements. The nonclassical characteristic of the problem is the joint optimization over the measurement process and the linear signal processing scheme. The problem is formulated as an optimizationproblem of a functional over a set of operator-valued measures and matrices. We prove existence of optimal linear filters and provide necessary and sufficient conditions for optimality.