Bayesian quantum estimation of the separation of two incoherent point sources

We examine the problem of estimating the separation between two arbitrarily close incoherent point sources from a quantum Bayesian perspective—that is, assuming the availability of a prior probability distribution function (PDF) for the separation. In particular, we consider both non-displaced and displaced half-Gaussian prior PDFs to evaluate the performance of Hermite–Gauss spatial mode demultiplexing (HG-SPADE) and direct imaging (DI). By employing the Bayesian minimum mean square error criterion, which is always attainable by a different kind of spatial demultiplexing, we compare the effectiveness of HG-SPADE and DI and analyze how variations in the parameters of the prior PDF influence the conditions under which one method outperforms the other.