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Author  |
Gebhart, V.; Gessner, M.; Smerzi, A. |
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Title |
Fundamental bounds for parameter estimation with few measurements |
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Journal Article |
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Year |
2024 |
Publication |
Physical Review Research |
Abbreviated Journal |
Phys. Rev. Res. |
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Volume |
6 |
Issue |
4 |
Pages |
043261 - 6pp |
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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. |
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Address |
[Gebhart, Valentin; Smerzi, Augusto] INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy |
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Publisher |
Amer Physical Soc |
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English |
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Notes |
WOS:001380753100003 |
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no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
6383 |
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