# A nearly optimal and robust protocol for nonlinear phase estimation using coherent states

## TL;DR

This paper introduces a nearly optimal, robust protocol for nonlinear phase estimation using coherent states, achieving sub-Heisenberg sensitivity and analyzing its performance under photon loss.

## Contribution

The authors present a new protocol for nonlinear phase estimation with coherent states that surpasses standard limits and demonstrate its robustness against photon loss.

## Key findings

- Sensitivity scales as N^{-3/2} with photon number N
- Protocol is nearly optimal compared to fundamental limits
- Robustness against photon loss demonstrated

## Abstract

We propose a protocol for the second-order nonlinear phase estimation with a coherent state as input and balanced homodyne detection as measurement strategy. The sensitivity is sub-Heisenberg limit, which scales as $N^{-3/2}$ for $N$ photons on average. By ruling out hidden resources in quantum Fisher information, the fundamental sensitivity limit is recalculated and compared to the optimal sensitivity of our protocol. In addition, we investigate the effect of photon loss on sensitivity, and discuss the robustness of measurement strategy. The results indicate that our protocol is nearly optimal and robust.