Quantum limited super-localization and super-resolution of a source pair in three dimensions

TL;DR

This paper extends quantum super-resolution techniques to simultaneously estimate the centroid and separation of a pair of incoherent sources in three dimensions, revealing fundamental trade-offs and achieving high-precision localization.

Contribution

It introduces a quantum estimation framework for joint localization of source pairs in 3D, analyzing the trade-offs and calculating quantum Fisher information for these parameters.

Findings

Quantum Fisher information for joint centroid and separation estimation calculated.

Fundamental trade-offs between localization tasks identified.

Simulations confirm theoretical estimation limits.

Abstract

A recent paper [Z. Yu and S. Prasad, "Quantum limited superresolution of an incoherent source pair in three dimensions," arXiv:1805.09227v2 [quant-ph] (2018)] considered the problem of quantum limited estimation of the separation vector for a pair of incoherent point sources in all three dimensions. Here we extend our analysis to treat the problem of simultaneously estimating the location of the centroid and the separation of the source pair, which is equivalent to localizing both sources simultaneously. We first calculate the quantum Fisher information for simultaneous pair centroid-separation estimation and then discuss the fundamental, estimation-theoretic trade-offs between the two tasks, which we confirm using simulations.