# Parity-Enhanced Quantum Optimal Measurements

## TL;DR

This paper introduces a quantum phase estimation protocol that leverages parity and particle number measurements to achieve optimal precision, demonstrating practical implementation in nonlinear interferometry and atomic condensates.

## Contribution

It proposes a new quantum phase estimation scheme with enhanced precision and practical implementation methods for arbitrary input states.

## Key findings

- Achieves phase estimation precision saturating the Cramer-Rao bound.
- Demonstrates implementation using nonlinear interferometry.
- Realizes nondemolition parity measurement in atomic condensates.

## Abstract

We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation protocol for arbitrary input states, through which the precision achieved is always higher than or equal to that obtained via the original input state. We also demonstrate the implementation of the proposed scheme using a nonlinear interferometry and the realization of the nondemolition parity measurement in atomic condensates.