Frequentist and Bayesian Quantum Phase Estimation

Year: 2018

Authors: Li Y., Pezzè L., Gessner M., Ren ZH., Li WD., Smerzi A.

Autors Affiliation: Shanxi Univ, Inst Theoret Phys, Taiyuan 030006, Peoples R China; Shanxi Univ, Dept Phys, State Key Lab Quantum Opt & Quantum Opt Devices, Collaborat Innovat Ctr Extreme Opt, Taiyuan 030006, Peoples R China; CNR, INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: 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.

Journal/Review: ENTROPY

Volume: 20 (9)      Pages from: 628-1  to: 628-22

More Information: This work was supported by the National Key R & D Program of China (No. 2017YFA0304500 and No. 2017YFA0304203), the National Natural Science Foundation of China (Grant No. 11874247), the 111 plan of China (No. D18001), the Hundred Talent Program of the Shanxi Province (2018), the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (No. KF201703), and the QuantEra project Q-Clocks. M.G. acknowledges support by the Alexander von Humboldt Foundation.
KeyWords: quantum metrology; Bayesian estimation; parameter estimation; signal parameter-estimation; bounds
DOI: 10.3390/e20090628

Citations: 39
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