Conservative classical and quantum resolution limits for incoherent imaging
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.
Keywords
Cite
@article{arxiv.1605.03799,
title = {Conservative classical and quantum resolution limits for incoherent imaging},
author = {Mankei Tsang},
journal= {arXiv preprint arXiv:1605.03799},
year = {2017}
}
Comments
12 pages, 2 figures. v2: focused on imaging, cleaned up the math, added new analytic and numerical results. v3: restructured and submitted