Coherence effects on estimating two-point separation

TL;DR

This paper analyzes how coherence affects the quantum Fisher information in estimating two-point source separation, revealing that partial knowledge can mitigate Rayleigh's curse, while complete ignorance reintroduces it.

Contribution

It provides a comprehensive analysis of the role of both magnitude and phase of coherence, clarifying conditions under which Rayleigh's curse can be avoided or reemerges.

Findings

Partial ignorance of coherence can break Rayleigh's curse.

Complete ignorance of coherence guarantees the resurgence of Rayleigh's curse.

Quantum Fisher information depends on both magnitude and phase of coherence.

Abstract

The quantum Fisher information (FI), when applied to the estimation of the separation of two point sources, has been shown to be non-zero in cases where the coherence between the sources are known. Although it has been claimed that ignorance of the coherence causes the quantum FI to vanish (a resurgence of Rayleigh's curse), a more complete analysis including both the magnitude and phase of the coherence parameter is given here. Partial ignorance of the coherence is shown to potentially break Rayleigh's curse, whereas complete ignorance guarantees its resurgence.