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arXiv · 2311.02066

Asymptotic behavior of continuous weak measurement and its application to real-time parameter estimation

Chungwei Lin·Yanting Ma·Dries Sels
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Abstract

The asymptotic quantum trajectory of weak continuous measurement for the magnetometer is investigated. The magnetometer refers to a setup where the field-to-estimate and the measured moment are orthogonal, and the quantum state is governed by the stochastic master equation which, in addition to a deterministic part, depends on the measurement outcomes. We find that the asymptotic behavior is insensitive to the initial state in the following sense: given one realization, the quantum trajectories starting from arbitrary initial states asymptotically converge to the {\em same} realization-specific {\em pure} state. For single-qubit systems, we are able to prove this statement within the framework of Probability Theory by deriving and analyzing an effective one-dimensional stochastic equation. Numerical simulations strongly indicate that the same statement holds for multi-qubit systems. Built upon this conclusion, we consider the problem of real-time parameter estimation whose feasibility hinges on the insensitivity to the initial state, and explicitly propose and test a scheme where the quantum state and the field-to-estimate are updated simultaneously.

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Chungwei Lin, Yanting Ma, Dries Sels. 2023-11-03. Asymptotic behavior of continuous weak measurement and its application to real-time parameter estimation. https://arxiv.org/abs/2311.02066

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