Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution

TL;DR

This paper demonstrates that using a collection of N-photon detection events with finite resolution in a squeezed-state interferometer can achieve phase estimation precision beyond the shot-noise limit, even with practical detector limitations.

Contribution

It introduces an analytical formula for optimal Fisher information scaling using finite-resolution photon counters in phase estimation.

Findings

Achieves ultimate phase estimation precision beyond shot-noise limit.

Derives an analytical expression for Fisher information scaling.

Shows finite-resolution detectors can still reach optimal precision.

Abstract

Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum Fisher information and scales as $\bar{n}^2$ for given input number of photons $\bar{n}$. However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of $N$-photon detection events for $N$ up to the resolution threshold $\sim \bar{n}$ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formula has been derived to obtain the best scaling of the Fisher information.