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

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 Cram\'er-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.