Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramer-Rao to Barankin

Year: 2023

Authors: Gessner M., Smerzi A.

Autors Affiliation: Univ Valencia, Dept Fis Teor, IFIC, CSIC, Carrer Dr Moliner 50, Valencia 46100, Spain; INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramer-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 130 (26)      Pages from: 260801-1  to: 260801-6

More Information: We would like to thank L. Pezz’e for fruitful discussions. This work was funded by MCIN/AEI/10.13039/501100011033 and the European Union NextGenerationEU PRTR fund [RYC2021-031094-I]. This work has been founded 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+). This work was supported by the European Commission through the H2020 QuantERA ERA-NET Cofund in Quantum Technologies project MENTA.
KeyWords: Useful Form; Distance; Metrics
DOI: 10.1103/PhysRevLett.130.260801

Citations: 2
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