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 operator...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.展开更多
基金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)+4 种基金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)Guizhou Provincial Theoretical Innovation Project(Grant No.GZLCLH-2025-ZX)。
文摘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.
