Bayesian quantum estimation of the separation of two incoherent point sources

TL;DR

This paper investigates quantum Bayesian methods for estimating the separation between two incoherent point sources, comparing SPADE and direct imaging techniques under different prior distributions to determine their relative effectiveness.

Contribution

It introduces a Bayesian framework for quantum estimation of source separation and analyzes the performance of SPADE versus direct imaging with various prior PDFs.

Findings

SPADE outperforms direct imaging in certain prior regimes

Bayesian MMSE varies with prior distribution parameters

Performance comparison depends on prior PDF characteristics

Abstract

We address the estimation problem of the separation of two arbitrarily close incoherent point sources from the quantum Bayesian point of view, i.e., when a prior probability distribution function (PDF) on the separation is available. For the non-dispalced and displaced half-Gaussian prior PDF, we compare the performance of SPADE and direct imaging (DI) with the Bayesian minimum mean square error and by varying the prior PDF's parameters we discuss the regimes of superiority of either SPADE or DI.