Linear Filtering with Quantum Mechanical Measurements

Filtering problems arising in the quantum electronics are investigated in the quantum mechanical framework. In particular the minimum varience linear estimator based on optimal selection of the present quantum measurement and optimal linear processing of past and present outcomes is found for vector signal processes. Under certain natural assumptions a separation theorum is for the filter is proven which leads to consideable simplification of the complexity of the filter. Examples from optical communication systems provide a recursive filters and illustrate the results.