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  • Open Access

Extracting filtered signal statistics of continuously measured quantum systems

Anthony Kiely1,2,3,* and Gabriel Landi4,5

  • *Contact author: AKiely@ucc.ie
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Phys. Rev. A 113, 032442 – Published 25 March, 2026

DOI: https://doi.org/10.1103/yxqg-93jz

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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Phys. Rev. A 113, 032442– Published 25 March, 2026
  • Received 14 July 2025
  • Accepted 9 March 2026
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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.

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