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oai:docta.ucm.es:20.500.14352/1367242026-05-14T00:24:56Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Romero Hervás, José Luis author Goldberg, A. Z. author Sanz Ortiz, Ángel Santiago author Hradil, Z. author Řeháček, J. author Sánchez Soto, Luis Lorenzo author 2025-08-20 Quantum Fisher information and the associated quantum Cramér-Rao bound (QCRB) are fundamental tools in frequentist quantum metrology, offering both analytical simplicity and practical precision limits for parameter estimation. The QCRB sets a lower bound on the mean square error (MSE) in the idealized limit of infinite measurement trials (ν → ∞). Here we perform a systematic expansion in powers of 1/ν to refine MSE estimates in realistic, finite-resource scenarios. These corrections reveal differences between measurements that appear equally optimal under the QCRB. They also help to distinguish among multiple optimal state families for estimating an unknown unitary transformation. Additionally, we explore the Bhattacharyya bound and its quantum counterpart, which constrain these corrections. Our results are relevant for preasymptotic metrology, enabling optimized protocols with limited resources without reliance on numerical simulations. Hervas, J.R., Goldberg, A.Z., Sanz, A.S., Hradil, Z., Řeháček, J., Sánchez-Soto, L.L., 2025. Higher-order corrections to the quantum Cramér-Rao bound. Phys. Rev. A 112, 022426. https://doi.org/10.1103/ltz3-163t 2469-9926 10.1103/ltz3-163t https://hdl.handle.net/20.500.14352/136724 2469-9934 https://dx.doi.org/10.1103/ltz3-163t https://journals.aps.org/pra/abstract/10.1103/ltz3-163t Higher-order corrections to the quantum Cramér-Rao bound