Conservative classical and quantum resolution limits for incoherent imaging

TL;DR

This paper establishes classical and quantum limits on the resolution of incoherent optical sources using minimax estimation, demonstrating the superiority of SPADE measurements over direct imaging at high photon counts.

Contribution

It introduces minimax-based resolution limits applicable to biased and unbiased estimators, extending beyond Cramér-Rao bounds, and confirms SPADE's advantage in high-photon regimes.

Findings

Minimax limits valid for all estimators.

SPADE outperforms direct imaging at high photon numbers.

Limits align with actual estimator behaviors.

Abstract

I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits proposed here, based on the worst-case error criterion and a Bayesian version of the Cram\'er-Rao bound, are valid for any biased or unbiased estimator and obey photon-number scalings that are consistent with the behaviors of actual estimators. These results prove that, from the minimax perspective, the spatial-mode demultiplexing (SPADE) measurement scheme recently proposed by Tsang, Nair, and Lu [Phys. Rev. X 6, 031033 (2016)] remains superior to direct imaging for sufficiently high photon numbers.