Achieving the Multi-parameter Quantum Cram\'er-Rao Bound with Antiunitary Symmetry

TL;DR

This paper introduces a novel approach using antiunitary symmetry to achieve the quantum Cramér-Rao bound simultaneously for multiple parameters, significantly improving precision in quantum metrology.

Contribution

It demonstrates that antiunitary symmetry can be exploited to optimize multi-parameter quantum estimation, achieving ultimate precision without trade-offs.

Findings

Achieves quantum Cramér-Rao bound for multiple parameters simultaneously

Improves estimation precision at least twofold over conventional methods

Provides experimental models demonstrating the approach

Abstract

The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared to single parameter estimation. To address this issue, optimizing the parameters encoding strategies with the aid of antiunitary symmetry is a novel and comprehensive approach. For demonstration, we propose two types of quantum statistical models exhibiting antiunitary symmetry in experiments. The results showcase the simultaneous achievement of ultimate precision for multiple parameters without any trade-off and the precision is improved at least twice compared to conventional encoding strategies. Our work emphasizes the significant potential of antiunitary symmetry in addressing multi-parameter estimation problems.