Quantum limited superresolution of an incoherent source pair in three dimensions

TL;DR

This paper extends quantum Fisher information analysis to three-dimensional incoherent source separation, demonstrating fundamental limits and proposing measurement bases to achieve quantum-limited superresolution.

Contribution

It calculates the 3D pair separation QFI, shows its equivalence to source localization QFI, and proposes measurement bases to attain these bounds.

Findings

QFI for 3D separation matches source localization QFI.

Proposed measurement bases can attain QFI bounds.

Simulations confirm experimental feasibility of quantum-limited superresolution.

Abstract

The error in estimating the separation of a pair of incoherent sources from radiation emitted by them and subsequently captured by an imager is fundamentally bounded below by the inverse of the corresponding quantum Fisher information (QFI) matrix. We calculate the QFI for estimating the full three-dimensional (3D) pair separation vector, extending previous work on pair separation in one and two dimensions. We also show that the pair-separation QFI is, in fact, identical to source localization QFI, which underscores the fundamental importance of photon-state localization in determining the ultimate estimation-theoretic bound for both problems. We also propose general coherent-projection bases that can attain the QFI in two special cases. We present simulations of an approximate experimental realization of such quantum limited pair superresolution using the Zernike basis, confirming the achievability of the QFI bounds.