Estimation of Random Signals based on Quantum Mechanical Measurements

We consider here the problem of estimating a scalar random signal based on quantum mechanical measurements, a situation frequently appearing in optical communication systems. We find the minimum variance estimator based on the combination of optimal observable selection at each time and optimal linear processing of past measurements. We compare this estimator with the one obtained by optimal selection of observables at each time independently. Under additional assumptions we demonstrate that the former estimator uses the same physical devices as the latter, followed by recursive classical filtering. The results are illustrated in the estimation of the real amplitude of a random coherent signal through quantum mechanical measure­ments in a single mode cavity with background thermal noise.