Frequentist and Bayesian Quantum Phase Estimation
Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise,...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/9/628 |
| _version_ | 1798039086428061696 |
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| author | Yan Li Luca Pezzè Manuel Gessner Zhihong Ren Weidong Li Augusto Smerzi |
| author_facet | Yan Li Luca Pezzè Manuel Gessner Zhihong Ren Weidong Li Augusto Smerzi |
| author_sort | Yan Li |
| collection | DOAJ |
| description | Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér–Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér–Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter. |
| first_indexed | 2024-04-11T21:49:03Z |
| format | Article |
| id | doaj.art-f081c32681754e30baea14a1b671c21d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T21:49:03Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f081c32681754e30baea14a1b671c21d2022-12-22T04:01:19ZengMDPI AGEntropy1099-43002018-08-0120962810.3390/e20090628e20090628Frequentist and Bayesian Quantum Phase EstimationYan Li0Luca Pezzè1Manuel Gessner2Zhihong Ren3Weidong Li4Augusto Smerzi5Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, ChinaQSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, ItalyQSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, ItalyInstitute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, ChinaInstitute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, ChinaQSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, ItalyFrequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér–Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér–Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.http://www.mdpi.com/1099-4300/20/9/628quantum metrologyBayesian estimationparameter estimation |
| spellingShingle | Yan Li Luca Pezzè Manuel Gessner Zhihong Ren Weidong Li Augusto Smerzi Frequentist and Bayesian Quantum Phase Estimation Entropy quantum metrology Bayesian estimation parameter estimation |
| title | Frequentist and Bayesian Quantum Phase Estimation |
| title_full | Frequentist and Bayesian Quantum Phase Estimation |
| title_fullStr | Frequentist and Bayesian Quantum Phase Estimation |
| title_full_unstemmed | Frequentist and Bayesian Quantum Phase Estimation |
| title_short | Frequentist and Bayesian Quantum Phase Estimation |
| title_sort | frequentist and bayesian quantum phase estimation |
| topic | quantum metrology Bayesian estimation parameter estimation |
| url | http://www.mdpi.com/1099-4300/20/9/628 |
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