Quantum Limited Superresolution of an Incoherent Source Pair in Three Dimensions

Area of Science:

• Quantum optics
• Estimation theory
• Optical imaging

Background:

• The precision of estimating source separation is limited by quantum mechanics.
• Previous work focused on 1D and 2D separation, leaving 3D unresolved.

Purpose of the Study:

• To calculate the quantum Fisher information (QFI) for 3D separation of incoherent sources.
• To establish the fundamental estimation-theoretic limits for source localization and separation.
• To propose methods for achieving these quantum limits in practice.

Main Methods:

• Quantum Fisher Information (QFI) matrix calculation for 3D separation vector.
• Demonstration of QFI equivalence between pair separation and source localization.
• Proposal of coherent-projection bases for QFI attainment.
• Simulations using Zernike basis for experimental validation.

Main Results:

• The QFI for 3D pair separation was derived, extending prior 1D/2D findings.
• Pair-separation QFI was shown to be identical to source localization QFI.
• General coherent-projection bases were proposed to reach QFI.
• Simulations confirmed the achievability of QFI bounds for quantum-limited superresolution.

Conclusions:

• The QFI provides the ultimate bound for 3D incoherent source separation and localization.
• Photon-state localization is key to achieving these fundamental estimation limits.
• Quantum-limited superresolution is experimentally feasible using proposed methods.