2026-07-18T13:31:22Zhttps://docta.ucm.es/rest/oai/request

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

Higher-order corrections to the quantum Cramér-Rao bound Romero Hervás, José Luis Goldberg, A. Z. Sanz Ortiz, Ángel Santiago Hradil, Z. Řeháček, J. Sánchez Soto, Luis Lorenzo IGA PRF 2025_005. NSF PHY-1748958. 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. 2026-05-13T17:46:23Z 2026-05-13T17:46:23Z 2025-08-20 journal article 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 eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-127781NB-I00/ES/CARACTERIZACION ROBUSTA DE ESTADOS CUANTICOS/ ApresSF http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International American Physical Society