期刊
ENTROPY
卷 20, 期 9, 页码 -出版社
MDPI
DOI: 10.3390/e20090628
关键词
quantum metrology; Bayesian estimation; parameter estimation
资金
- National Key R & D Program of China [2017YFA0304500, 2017YFA0304203]
- National Natural Science Foundation of China [11874247]
- 111 plan of China [D18001]
- Hundred Talent Program of the Shanxi Province
- Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices [KF201703]
- Alexander von Humboldt Foundation
- QuantEra project Q-Clocks
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 Cramer-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 Cramer-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.
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