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Published March 27, 2023 | metadata_only
Journal Article Embargoed

Fundamental quantum limit for linear measurements with instability


The fundamental quantum limit, or the quantum Cramér-Rao bound, defines the sensitivity limit for quantum measurements. For linear measurement systems, such as gravitational-wave detectors, it is inversely proportional to the noise spectrum of the dynamical variable that couples to the measured signal. Defining a physically meaningful spectrum, however, requires that the system is stable and a steady state exists. We relax such a stability requirement and prove that the fundamental quantum limit can be derived simply by considering the open-loop dynamics in the Fourier domain.

Additional Information

© 2023 Author(s). Published under an exclusive license by AIP Publishing. We would like to acknowledge the MQM group and LIGO QNWG for valuable discussions. H.M. was supported by the State Key Laboratory of Low Dimensional Quantum Physics and the start-up fund from Tsinghua University. J.B. was supported by the Institute for Laser Physics at Hamburg University. H.N. acknowledges the supports from the University of New South Wales. Y.C. has been funded by Simons Fundation. Author Contributions. Haixing Miao: Writing – original draft (lead). Joe Bentley: Investigation (equal); Writing – review & editing (equal). Hendra Nurdin: Formal analysis (equal); Investigation (equal); Writing – review & editing (equal). Yanbei Chen: Investigation (equal). DATA AVAILABILITY. The data that support the findings of this study are available within the article. The authors have no conflicts to disclose.

Additional details

August 22, 2023
August 22, 2023