Stochastic waveform estimation at the fundamental quantum limit

TL;DR

This paper derives the fundamental quantum limit for estimating stochastic waveforms and proposes an optimal non-Gaussian protocol, advancing quantum sensing in physics research.

Contribution

It introduces the extended channel quantum Cramér-Rao bound for stochastic waveform estimation and identifies non-Gaussian strategies as optimal under realistic conditions.

Findings

Derived the fundamental quantum limit for stochastic waveform estimation.

Identified non-Gaussian states and measurements as necessary for optimality in lossy regimes.

Proposed potential applications in quantum gravity, gravitational waves, and dark matter detection.

Abstract

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well-understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement, but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit, the extended channel quantum Cram\'er-Rao bound, and the optimal protocol that attains it. In the experimentally relevant regime where losses dominate, we prove that non-Gaussian state preparation and measurements are required for optimality. We discuss how this non-Gaussian protocol could improve searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.