Quantum Estimation of Parameters of Classical Spacetimes

TL;DR

This paper establishes a fundamental quantum limit on measuring parameters of classical spacetimes, providing a background-independent uncertainty relation applicable to various gravitational measurement scenarios.

Contribution

It formulates a quantum Cramer-Rao bound for spacetime parameter estimation using locally covariant quantum field theory, a novel approach in quantum gravity measurement.

Findings

Derived a universal quantum uncertainty relation for spacetime parameters

Applied the bound to gravitational wave detection with electromagnetic probes

Discussed implications for gravimetry and cosmology

Abstract

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a 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 that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.