Fundamental bounds for parameter estimation with few measurements

Year: 2024

Authors: Gebhart V., Gessner M., Smerzi A.

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

Abstract: Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or low signal-to-noise ratios, the meaning of common frequentist bounds, such as the Cram & eacute;r-Rao bound (CRB), becomes questionable. Here, we discuss a different (Barankin-like) approach to derive the conditions for the existence of optimal estimators and calculate their variance, for any number of measurement repetitions. We elaborate on connections to the shot-noise limit and the Kitaev phase estimation algorithm and derive an extended Cram & eacute;r-Rao bound that is compatible with a finite variance in situations where the Barankin bound (BaB) is undefined. Finally, we show an exemplary numerical confrontation between frequentist and Bayesian approaches to parameter estimation.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 6 (4)      Pages from: 43261-1  to: 43261-6

More Information: This work was supported by the European Commission through the H2020 Quant ERA ERA-NET Co-fund in Quantum Technologies project MENTA and received funding under the Horizon Europe programme HORIZONCL4-2022-QUANTUM-02-SGA via the project 101113690 (PASQuanS2.1) . This work was funded by MCIN/AEI/10.13039/501100011033 and the European Union ’NextGenerationEU’ PRTR fund [RYC2021-031094-I] . This work has been financially supported by the Ministry for Digital Transformation and of Civil Service of the Spanish Government through the QUANTUM ENIA project call-Quantum Spain project, and by the European Union through the Recovery, Transformation and Resilience Plan-NextGenerationEU within the framework of the Digital Spain 2026 Agenda. This work has been supported by the CSIC Interdisciplinary Thematic Platform (PTI +) on Quantum Technologies (PTI-QTEP +) .
KeyWords: Useful Form; Threshold; Information
DOI: 10.1103/PhysRevResearch.6.043261