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

• URL: http://arxiv.org/abs/2311.02066v1
• Date: Fri, 3 Nov 2023 17:50:45 GMT
• Title: Asymptotic behavior of continuous weak measurement and its application to real-time parameter estimation
• Authors: Chungwei Lin and Yanting Ma and Dries Sels
• Abstract summary: The quantum trajectory of weak continuous measurement for the magnetometer is investigated. We find that the behavior is insensitive to the initial state in the following sense: given one realization, the quantum trajectories starting from arbitrary initial statesally converge to the em same realization-specific em pure state.
• Score: 4.329298109272387
• License: http://creativecommons.org/licenses/by/4.0/
• 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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