Quantum limit to subdiffraction incoherent optical imaging. III. Numerical analysis

TL;DR

This paper numerically verifies the quantum limit for subdiffraction incoherent optical imaging and assesses the optimality of SPADE measurements for estimating object moments.

Contribution

It provides a numerical analysis confirming the quantum scaling law for nonzero object sizes and evaluates SPADE's near-optimal performance.

Findings

Quantum scaling law holds for finite object sizes.

SPADE measurement closely approaches the quantum limit.

Numerical bounds support SPADE's optimality for low-order moments.

Abstract

To investigate the fundamental limit to far-field incoherent imaging, the prequels to this work [M. Tsang, Phys. Rev. A 99, 012305 (2019); 104, 052411 (2021)] have studied a quantum lower bound on the error of estimating an object moment and proved a scaling law for the bound with respect to the object size. As the scaling law was proved only in the asymptotic limit of vanishing object size, this work performs a numerical analysis of the quantum bound to verify that the law works well for nonzero object sizes in reality. We also use the numerical bounds to study the optimality of a measurement called spatial-mode demultiplexing or SPADE, showing that SPADE not only follows the scaling but is also numerically close to being optimal, at least for low-order moments.