Existence of unbiased estimators in discrete quantum systems
The Cramér-Rao bound serves as a crucial lower limit for the mean square error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator. In contrast, Bhattacharyya bounds...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023060 |
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| author | Javier Navarro Ricard Ravell Rodríguez Mikel Sanz |
| author_facet | Javier Navarro Ricard Ravell Rodríguez Mikel Sanz |
| author_sort | Javier Navarro |
| collection | DOAJ |
| description | The Cramér-Rao bound serves as a crucial lower limit for the mean square error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator. In contrast, Bhattacharyya bounds offer a more robust estimation framework with respect to prior accuracy by introducing additional constraints on the estimator. In this work, we examine divergences that arise in the computation of these bounds and establish the conditions under which they remain valid. Notably, we show that when the number of constraints exceeds the number of measurement outcomes, an estimator with finite variance typically does not exist. Furthermore, we systematically investigate the properties of these bounds using paradigmatic examples, comparing them to the Cramér-Rao and Bayesian approaches. |
| format | Article |
| id | doaj-art-9d661802b89a4ee8b9bb7b891dd3db82 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-9d661802b89a4ee8b9bb7b891dd3db822025-08-20T03:18:46ZengAmerican Physical SocietyPhysical Review Research2643-15642025-04-017202306010.1103/PhysRevResearch.7.023060Existence of unbiased estimators in discrete quantum systemsJavier NavarroRicard Ravell RodríguezMikel SanzThe Cramér-Rao bound serves as a crucial lower limit for the mean square error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator. In contrast, Bhattacharyya bounds offer a more robust estimation framework with respect to prior accuracy by introducing additional constraints on the estimator. In this work, we examine divergences that arise in the computation of these bounds and establish the conditions under which they remain valid. Notably, we show that when the number of constraints exceeds the number of measurement outcomes, an estimator with finite variance typically does not exist. Furthermore, we systematically investigate the properties of these bounds using paradigmatic examples, comparing them to the Cramér-Rao and Bayesian approaches.http://doi.org/10.1103/PhysRevResearch.7.023060 |
| spellingShingle | Javier Navarro Ricard Ravell Rodríguez Mikel Sanz Existence of unbiased estimators in discrete quantum systems Physical Review Research |
| title | Existence of unbiased estimators in discrete quantum systems |
| title_full | Existence of unbiased estimators in discrete quantum systems |
| title_fullStr | Existence of unbiased estimators in discrete quantum systems |
| title_full_unstemmed | Existence of unbiased estimators in discrete quantum systems |
| title_short | Existence of unbiased estimators in discrete quantum systems |
| title_sort | existence of unbiased estimators in discrete quantum systems |
| url | http://doi.org/10.1103/PhysRevResearch.7.023060 |
| work_keys_str_mv | AT javiernavarro existenceofunbiasedestimatorsindiscretequantumsystems AT ricardravellrodriguez existenceofunbiasedestimatorsindiscretequantumsystems AT mikelsanz existenceofunbiasedestimatorsindiscretequantumsystems |