Extracting filtered signal statistics of continuously measured quantum systems
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Date
2026-03-25
Authors
Kiely, Anthony
Landi, Gabriel
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Abstract
The joint state of a continuously monitored quantum system and the classical filtered measurement record has recently been shown to be described by a quantum Fokker-Planck master equation [Phys. Rev. Lett. 129, 050401 (2022)]. We present a deterministic approach to compute the steady state of the system and detector. The method is shown to become particularly efficient in the absence of feedback, which we exploit to develop a perturbative approach valid for weak feedback. We show that through this method we can extract the full counting statistics of the signal, the quantum-classical mutual information between the system and signal, and the Fisher information of the signal, which can be used for sensing applications. Our results are illustrated with both single-qubit models and the spin chains governed by the one-dimensional transverse field Ising model or the Lipkin-Meshkov-Glick model.
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© 2026, the Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Keywords
Deterministic approach , Filtered signals , Fisher information matrix , Fokker Planck , Fokker Planck equation , Full counting statistics , Master equations , Perturbative approach , Quantum optics , Quantum system , Quantum-classical , Qubits , Signal processing , Signals statistics , Steady state , [Physics]
Citation
Kiely, A & Landi, G 2026, 'Extracting filtered signal statistics of continuously measured quantum systems', Physical Review A, vol. 113, no. 3, 032442, pp. 1-12. https://doi.org/10.1103/yxqg-93jz
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