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Quantum Cramér-Rao Precision Limit of Noisy Continuous Sensing

Dayou Yang1,2,3,*, Moulik Ketkar3,4, Koenraad Audenaert3, Susana F. Huelga3,†, and Martin B. Plenio3,‡

  • *Contact author: dayou.yang@ustc.edu.cn
  • †Contact author: susana.huelga@uni-ulm.de
  • ‡Contact author: martin.plenio@uni-ulm.de
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Phys. Rev. Lett. 136, 070802 – Published 18 February, 2026

DOI: https://doi.org/10.1103/ltfw-4fwn

Abstract

Quantum sensors hold considerable promise for precision measurement, yet their capabilities are inherently constrained by environmental noise. A fundamental task in quantum sensing is determining the precision limit of noisy sensor devices. For continuously monitored quantum sensors, characterizing the optimal precision in the presence of environments other than the measurement channel is an outstanding open theoretical challenge, due to the infinite-dimensional nature of the sensor output field and the complex temporal correlation of the photons therein. Here, we establish a numerically efficient method to determine the quantum Cramér-Rao bound for continuously monitored quantum sensors subject to general environmental noise—Markovian or non-Markovian, and showcase its application with paradigmatic models of continuously monitored quantum sensors. Applicable to both constant-parameter and waveform estimation, our method provides a rigorous and practical framework for assessing and enhancing the sensor performance in realistic settings, with broad applications across experimental quantum physics.

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Phys. Rev. Lett. 136, 070802– Published 18 February, 2026
  • Received 23 April 2025
  • Revised 18 November 2025
  • Accepted 20 January 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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