Evaluating the quantum optimal biased bound in a unitary evolution process

Shoukang Chang; Wei Ye; Xuan Rao; Huan Zhang; Liqing Huang; Mengmeng Luo; Yuetao Chen; Qiang Ma; Yunbin Yan; Lu Wang; Shaoyan Gao

Results in Physics (Jun 2024)

Evaluating the quantum optimal biased bound in a unitary evolution process

Shoukang Chang,
Wei Ye,
Xuan Rao,
Huan Zhang,
Liqing Huang,
Mengmeng Luo,
Yuetao Chen,
Qiang Ma,
Yunbin Yan,
Lu Wang,
Shaoyan Gao

Affiliations

Shoukang Chang: MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China; Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, 20133 Milan, Italy
Wei Ye: School of Information Engineering, Nanchang Hangkong University, Nanchang 330063, China; Corresponding authors.
Xuan Rao: School of Information Engineering, Nanchang Hangkong University, Nanchang 330063, China
Huan Zhang: School of Physics, Sun Yat-sen University, Guangzhou 510275, China
Liqing Huang: MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Mengmeng Luo: Department of Physics, Xi’an Jiaotong University City College, Xi’an 710018, China
Yuetao Chen: MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Qiang Ma: MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Yunbin Yan: Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050035, China
Lu Wang: Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050035, China
Shaoyan Gao: MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China; Corresponding authors.

Journal volume & issue: Vol. 61
p. 107741

Abstract

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Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramér–Rao bound (QCRB) based on unbiased estimators to finish this task. Nevertheless, most actual estimators are usually biased in the limited number of trials. For this reason, we introduce two effective error bounds for biased estimators based on a unitary evolution process in the framework of the quantum optimal biased bound. Furthermore, we show their estimation performance by two specific examples of the unitary evolution process, including the phase encoding and the SU(2) interferometer process. Our findings will provide an useful guidance for finding the precision limit of unknown parameters.

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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