Moment-based superresolution: Formalism and applications

TL;DR

This paper introduces a superresolution method for estimating the separation between two thermal sources using only the average of a single observable, achieving optimal sensitivity and saturating the quantum Cramér-Rao bound even with noise.

Contribution

The work presents a simple, practical superresolution protocol based on average measurements, with optimal observables for thermal sources, and analyzes its performance under noise and different measurement schemes.

Findings

Method saturates the quantum Cramér-Rao bound.

Optimal observables can be constructed for arbitrary thermal sources.

Performance remains robust under noise and low signal conditions.

Abstract

Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.