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Quantum Estimation of the Classical Gravitational Field



Emanuel H. Knill, T. G. Downes, G. J. Milburn, C. M. Caves, J. R. van Meter


Here we describe a quantum limit to measurement of the classical gravitational field. Specifically, we formulate the quantum Cramer-Rao lower bound for estimating the single parameter in any one- parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation applicable to all globally hyperbolic spacetimes. Among other examples, we apply our method to a laser-interferometric gravitational wave detector and derive the expected shot-noise limit. Other applications are discussed, from terrestrial gravimetry to cosmology.
Physical Review D (Particles, Fields, Gravitation and Cosmology)


Cramer-Rao bound, general covariance, general relativity, quantum field theory, quantum information


Knill, E. , Downes, T. , Milburn, G. , Caves, C. and van, J. (2017), Quantum Estimation of the Classical Gravitational Field, Physical Review D (Particles, Fields, Gravitation and Cosmology), [online], (Accessed February 23, 2024)
Created November 6, 2017, Updated May 19, 2020