# Experimental Joint Estimation of Phase and Phase Diffusion Via Deterministic Bell Measurements

## TL;DR

This paper shows how using entangled measurements can improve the precision of estimating phase and its fluctuations in quantum metrology.

## Contribution

The novel contribution is the experimental demonstration of joint phase and phase-diffusion estimation using deterministic Bell measurements.

## Key findings

- Deterministic Bell measurements outperform separable strategies in joint phase and phase-diffusion estimation.
- Entangling measurements enable reaching the ultimate precision limit in multi-parameter quantum metrology.
- A linear optical network was used to implement parameter encoding and Bell measurements.

## Abstract

Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase‐diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase and phase diffusion has emerged as an effective approach, transforming the problem into a multi‐parameter estimation task. However, the incompatibility between optimal measurements for different parameters prevents single‐copy measurements from reaching the fundamental precision limits defined by the quantum Cramér–Rao bound. Meanwhile, collective measurements performed on multiple identical copies can mitigate this incompatibility and thus enhance the precision of joint parameter estimation. This work experimentally demonstrates joint phase and phase‐diffusion estimation using deterministic Bell measurements on a two‐qubit system. A linear optical network is employed to implement both parameter encoding and deterministic Bell measurements, achieving improved estimation precision compared to any separable measurement strategy. This work proposes a new framework for phase estimation under phase‐diffusive noise and underscores the substantial advantages of collective measurements in multi‐parameter quantum metrology.

This work employs Bell measurement, a form of entangling measurement, to estimate both the phase and its fluctuations in an optical interferometer. By incorporating a novel quantum effect at the measurement stage, the proposed method achieves the ultimate precision limit and demonstrates the significant potential of entangling measurements in multi‐parameter estimation.