Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach

TL;DR

This paper rigorously establishes the quantum limit for subdiffraction incoherent optical imaging, demonstrating that spatial-mode demultiplexing can achieve this limit and outperform classical direct imaging methods.

Contribution

It provides a rigorous proof of the quantum limit using infinite-dimensional analysis and shows SPADE's optimality in reaching this limit.

Findings

SPADE with one or two modes achieves the quantum limit.

Classical direct imaging is significantly less effective.

The quantum limit applies to a broader class of moments.

Abstract

In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing (SPADE) with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.