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International Journal of Theoretical Physics

Enhancing the Precision of Phase Estimation by Weak Measurement and Quantum Measurement Reversal in High Dimensional Quantum System

Qiong Wang, Zhi He

Published Oct 9, 2018• 10 citations
Publisher
DOI
10.1007/s10773-018-3915-z

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The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement (WM) and quantum measurement reversal (QMR). We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.
Abstract We investigate the effect of the weak measurement (WM) and quantum measurement reversal (QMR) on the improvement of the precision of parameter estimation for a qubit interacting with various non-Markovian decoherence sources: amplitude damping, dephasing damping and random unitary damping, respectively. We derive the exact expressions of the optimal quantum Fisher information, show explicitly that the WM and QMR operation indeed helps for enhancing the precision of parameter estimation from amplitude damping and phase damping, but not for random unitary damping. In particular, we found that the enhancement effect is independent of the specific form of the spectral density of the reservoir, which extends the applicable scope of the WM and QMR approach.
Abstract Quantum metrology has emerged as a crucial paradigm for enhancing measurement sensitivity beyond classical limits. While standard weak measurement and static biased phase methods can effectively amplify extremely small signals, they fundamentally suffer from a trade-off between postselection probability and linear response range, leaving them vulnerable to parameter drift. Motivated by realistic experimental applications such as measuring optical birefringence or thickness using a polarization-frequency Sagnac interferometer, we propose an adaptive biased weak measurement (ABWM) scheme that combines the sensitivity enhancement of biased weak measurement with a feedback-assisted adjustment of the bias phase. By dynamically updating the bias phase in response to measurement outcomes, the system can track slow parameter variations and maintain nearoptimal estimation precision. Numerical simulations under technical noise demonstrate reliable convergence from multiple random initial bias phases and show that the proposed adaptive- β strategy achieves more accurate dynamic tracking than standard weak measurement and static biased weak measurement. Our results suggest that ABWM provides a flexible and resource-efficient strategy for high-precision quantum metrology in realistic experimental scenarios.