Fundamental relations between measurement, radiation, and decoherence in gravitational wave laser interferometer detectors

Belinda Pang and Yanbei Chen
Phys. Rev. D 99, 124016 – Published 11 June 2019

Abstract

As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection—specifically the quantum Cramer-Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state’s quantum Fisher information (QFI) with respect to the parameter [Helstrom, J. Stat. Phys. 1, 231 (1969)]. Identifying the QFI requires knowing the interaction between the quantum probe and the signal, which was rigorously derived for GW interferometer detectors in Pang and Chen [Phys. Rev. D 98, 124006 (2018)]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore we derive explicit reciprocity relations involving the QFI that summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector’s quantum fluctuations are proportional to the QFI, and therefore are inversely proportional to its FQL. Similarly, the detector’s decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.

  • Figure
  • Received 22 March 2019

DOI:https://doi.org/10.1103/PhysRevD.99.124016

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsQuantum Information, Science & Technology

Authors & Affiliations

Belinda Pang and Yanbei Chen

  • Theoretical Astrophysics and Walter Burke Institute for Theoretical Physics, M/C 350-17, California Institute of Technology, Pasadena, California 91125, USA

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Issue

Vol. 99, Iss. 12 — 15 June 2019

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