Superresolution at the quantum limit beyond two point sources

TL;DR

This paper develops a general quantum measurement framework using symmetry principles to achieve superresolution beyond classical limits for multiple point sources, extending previous two-source results.

Contribution

It introduces a novel symmetry-based approach for constructing quantum measurements that attain the quantum Cramer-Rao bound for multiple symmetric point sources.

Findings

Achieves quantum limits of estimation for more than two point sources.

Utilizes quantum computing techniques like Fourier transforms for measurement implementation.

Extends superresolution techniques beyond previous two-source constraints.

Abstract

Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point sources (with a known centroid) was shown to achieve the quantum Cramer-Rao bound. This work made implicit use of reflection symmetry of the sources. Here we present a framework that uses more general symmetry in a constellation to construct a quantum measurement that achieves the quantum Cramer-Rao bound in estimation of parameters. We show how this technique can be used to estimate parameters simultaneously in symmetric point-source constellations with more than two point sources. In order to use symmetry explicitly, we make use discrete point spread functions in momentum space that maintain this symmetry. This framework allows us to use techniques from quantum computing such as Fourier transforms and linear optical circuits to implement the optimal measurement. To our knowledge, this is first work that shows for more than two point sources achievable quantum limits of estimation and modal transformations.