Optical phase estimation in the presence of phase-diffusion

TL;DR

This paper investigates the fundamental quantum limits of optical phase estimation under phase diffusion noise, identifying near-optimal detection strategies and how precision scales with energy and noise levels.

Contribution

It derives approximate scaling laws for quantum Fisher information and optimal squeezing in noisy conditions, and shows homodyne detection's near-optimality across noise regimes.

Findings

Homodyne detection is nearly optimal for very small and large noise.

Quantum Fisher information scales with energy and noise levels.

Optimal squeezing fraction depends on total energy and noise.

Abstract

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for the quantum Fisher information and the optimal squeezing fraction in terms of the overall total energy and the amount of noise. We also found that homodyne detection is a nearly optimal detection scheme in the limit of very small and large noise.