Photonic Metrology with Hierarchic Quantum Frequentist Bounds

Quantum metrology establishes fundamental precision limits for parameter estimation, yet standard Quantum Cramér‐Rao Bound (QCRB) becomes insufficient in the finite‐data regime. In this article, the QCRB is systematically tighten using a hybrid classical‐quantum framework by incorporating generalized unbiasedness constraints through test observables. These frequentist bounds form a hierarchy converging asymptotically to the QCRB as more measurements are performed. These hierarchical frequentist bounds are validated for single‐qubit phase estimation on a photonic platform.