Optimal quantum superresolution for full distance between incoherent optical sources in two dimensions

TL;DR

This paper explores the fundamental limits of estimating the full distance between two incoherent optical sources in two dimensions, surpassing the Rayleigh criterion by leveraging quantum metrology and source alignment strategies.

Contribution

It derives the ultimate quantum estimation precision for the full distance between sources and introduces a scheme to enhance accuracy through source orientation alignment.

Findings

Quantum estimation precision remains nonzero as distance approaches zero.

Alignment of sources along specific directions improves estimation accuracy.

Results are demonstrated with Gaussian point-spread functions.

Abstract

The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing precision in estimating the separation between a pair of closely located incoherent point sources. For two-dimensional optical systems, the quantum superresolution has been studied for the Cartesian components of separation between two incoherent point sources. However, the precision limit of estimating the full distance between two point sources remains unknown so far. In this paper, we investigate the estimation precision of the full distance between two incoherent point sources with arbitrary intensities in a two-dimensional imaging system. Through the multiparameter quantum estimation theory, we obtain the ultimate estimation precision for the distance and show that it remains nonzero when the distance approaches zero, which surpasses the Rayleigh criterion. We further show the dependence of the estimation precision on the relative orientation between the two point sources, which leads to a novel scheme that can enhance the precision by aligning the sources along proper directions if the point-spread functions are not circularly symmetric, and the enhancement is determined by the extent to which the point-spread functions deviate from circular symmetry. Finally, the results are illustrated by incoherent sources with Gaussian point-spread functions.