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Recent inquiries into optical communication have raised questions as to the validity of classical detection and estimation theory for weak light fields. Helstrom 1 proposed that the axioms of quantum mechanics be incorporated into a quantum approach to optical estimation and detection. In this paper, we discuss two important results, the quantum equivalent of the minimum-mean-square-error (MMSE) estimator and the quantum Cramér-Rao bound for estimation of the parameters of an electromagnetic field. The first result, a new one, is applied to linear modulation. We show that homodyning is the optimal demodulation scheme in that case. Parallels to the classical MMSE estimator are drawn. The Cramér-Rao bound, first derived in the quantum ease by Helstrom 1, is applied to specific estimation problems. Details are left to the references, but interesting results are presented.
Stewart D. Personick (1971) studied this question.