An optimization problem from linear filtering with quantum measurements (Q1108253)

The paper studies the linear estimation problem for a discrete-time vector signal process based on quantum mechanical measurements. In the vector case, the well-known quantum mechanical problem of simultaneous measurements arises and the concept of generalized quantum measurements has to be used. The problem consists in the joint optimization of the measurement process and of the signal processing coefficients. Necessary and sufficient conditions for optimality as well as results on the existence of optimal linear filters are provided exploiting a suitable formulation of the given problem as an optimization problem.