中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10307-010307.doi: 10.1088/1674-1056/ae29fe

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Impact of decoherence on the metrological advantage of weak-value amplification

Yu-Han Yan(严雨涵)2,†, Yan-Ping Tan(谭艳萍)1,†, Yan-Yan Lu(陆艳艳)1,á, Shao-Jie Xiong(熊少杰)1,§, and Zhe Sun(孙哲)1,¶   

  1. 1 College of Big Data and Intelligent Engineering, Guizhou University of Commerce, Guiyang 550014, China;
    2 School of Physics, Hangzhou Normal University, Hangzhou 310036, China
  • 收稿日期:2025-10-06 修回日期:2025-11-13 接受日期:2025-12-09 发布日期:2026-01-05
  • 通讯作者: Yan-Yan Lu, Shao-Jie Xiong, Zhe Sun E-mail:xiaoguai@gzsxy361.wecom.work;202410003@gzcc.edu.cn;sunzhe@hznu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12175052 and 12405010), Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of China (Grant No. LHZSD24A050001), the Hangzhou Leading Youth Innovation and Entrepreneurship Team Project (Grant No. TD2024005), the HZNU scientific Research and Innovation Team Project (Grant No. TD2025003), the Guizhou Province Higher Education Teaching Content and Curriculum System Reform Project (Grant No. 2023233), the Guizhou Education Department Young Talent in Science and Technology Program (Grant Nos. QianJiaoJi[2024]174 and QianJiaoJi[2024]178), and Guizhou Provincial Theoretical Innovation Project (Grant No. GZLCLH-2025-ZX).

Impact of decoherence on the metrological advantage of weak-value amplification

Yu-Han Yan(严雨涵)2,†, Yan-Ping Tan(谭艳萍)1,†, Yan-Yan Lu(陆艳艳)1,á, Shao-Jie Xiong(熊少杰)1,§, and Zhe Sun(孙哲)1,¶   

  1. 1 College of Big Data and Intelligent Engineering, Guizhou University of Commerce, Guiyang 550014, China;
    2 School of Physics, Hangzhou Normal University, Hangzhou 310036, China
  • Received:2025-10-06 Revised:2025-11-13 Accepted:2025-12-09 Published:2026-01-05
  • Contact: Yan-Yan Lu, Shao-Jie Xiong, Zhe Sun E-mail:xiaoguai@gzsxy361.wecom.work;202410003@gzcc.edu.cn;sunzhe@hznu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12175052 and 12405010), Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of China (Grant No. LHZSD24A050001), the Hangzhou Leading Youth Innovation and Entrepreneurship Team Project (Grant No. TD2024005), the HZNU scientific Research and Innovation Team Project (Grant No. TD2025003), the Guizhou Province Higher Education Teaching Content and Curriculum System Reform Project (Grant No. 2023233), the Guizhou Education Department Young Talent in Science and Technology Program (Grant Nos. QianJiaoJi[2024]174 and QianJiaoJi[2024]178), and Guizhou Provincial Theoretical Innovation Project (Grant No. GZLCLH-2025-ZX).

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摘要： We present a theoretical investigation of weak-value amplification (WVA) under decoherence, quantifying its metrological capabilities through the quantum Fisher information (QFI). By modeling decoherence via Kraus operators acting before and after the weak measurement interaction, we derive exact expressions for the QFI governing parameter estimation of a weak coupling strength. These analytical results reveal the fundamental limitation imposed by decoherence on the QFI achievable via WVA. From these results, the optimal post-selection state that maximizes the QFI can be derived for different noise environments. Through paradigmatic examples, including amplitude damping and depolarizing channels, we demonstrate a key distinction: the optimal post-selection evolves with the noise strength in the amplitude damping channel, but is fixed in the depolarizing channel. This work provides both theoretical insights and practical guidance for optimizing metrological schemes based on WVA in realistic decoherent environments.

关键词: quantum metrology, weak-value amplification, quantum Fisher information

Abstract: We present a theoretical investigation of weak-value amplification (WVA) under decoherence, quantifying its metrological capabilities through the quantum Fisher information (QFI). By modeling decoherence via Kraus operators acting before and after the weak measurement interaction, we derive exact expressions for the QFI governing parameter estimation of a weak coupling strength. These analytical results reveal the fundamental limitation imposed by decoherence on the QFI achievable via WVA. From these results, the optimal post-selection state that maximizes the QFI can be derived for different noise environments. Through paradigmatic examples, including amplitude damping and depolarizing channels, we demonstrate a key distinction: the optimal post-selection evolves with the noise strength in the amplitude damping channel, but is fixed in the depolarizing channel. This work provides both theoretical insights and practical guidance for optimizing metrological schemes based on WVA in realistic decoherent environments.

Key words: quantum metrology, weak-value amplification, quantum Fisher information

中图分类号:  (Foundations of quantum mechanics; measurement theory)

  • 03.65.Ta
03.65.Yz (Decoherence; open systems; quantum statistical methods)