Photonic Metrology with Hierarchic Quantum Frequentist Bounds

Year: 2025

Authors: Liu XZ., Yang YH., Gessner M., Smerzi A., Li WD., Yang X., Luo MX.

Autors Affiliation: Southwest Jiaotong Univ, Sch Informat Sci & Technol, Chengdu 610031, Peoples R China; Univ Valencia, Inst Fis Corpuscular IFIC, CSIC, C Dr Moliner 50, Burjassot 46100, Valencia, Spain; UV, Dept Fis Teor, C Dr Moliner 50, Burjassot 46100, Valencia, Spain; CNR, INO, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Shenzhen Technol Univ, Ctr Intense Laser Applicat Technol, Shenzhen Key Lab Ultraintense Laser & Adv Mat Tech, Shenzhen 518118, Peoples R China; Shenzhen Technol Univ, Coll Engn Phys, Shenzhen 518118, Peoples R China; Hefei Natl Lab, Hefei 230088, Anhui, Peoples R China.

Abstract: Quantum metrology establishes fundamental precision limits for parameter estimation, yet standard Quantum Cram & eacute;r-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.

Journal/Review: ADVANCED PHOTONICS RESEARCH

More Information: National Natural Science Foundation of China (nos. 62172341, 12204386, 12075159), Sichuan Natural Science Foundation (no. 2023NSFSC0447), and Interdisciplinary Research of Southwest Jiaotong University China (no. 2682022KJ004), Guangdong Basic and Applied Basic Research Foundation (No.2025A1515011840), and the Natural Science Foundation of Top Talent of SZTU (GDRC202202). G.M. is supported by the project PID2023-152724NA-I00, with funding from MCIU/AEI/10.13039/501100011033 and FSE+, by the project CNS2024-154818 with funding by MICIU/AEI/10.13039/501100011033, by the project CIPROM/2022/66 with funding by the Generalitat Valenciana, and by the Ministry of Economic Affairs and Digital Transformation of the Spanish Government through the QUANTUM ENIA Project call-QUANTUM SPAIN Project, by the European Union through the Recovery, Transformation and Resilience Plan-NextGenerationEU within the framework of the Digital Spain 2026 Agenda, and by the CSIC Interdisciplinary Thematic Platform (PTI+) on Quantum Technologies (PTI-QTEP+), and the project CEX2023-001292-S funded by MCIU/AEI.AS was supported by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies project MENTA. The authors thank reviewers for constructive comments.
KeyWords: photonic experiment; quantum frequentist bounds; quantum metrology
DOI: 10.1002/adpr.202500199