Achieving the fundamental quantum limit of linear waveform estimation

TL;DR

This paper establishes the fundamental quantum limit for linear waveform estimation, resolving previous gaps between known bounds and demonstrating how to attain optimal sensitivity with nonstationary measurements, with applications to gravitational-wave detection.

Contribution

It introduces the waveform-estimation Holevo Cramér-Rao Bound and shows how to achieve it using nonstationary measurements, advancing quantum sensing precision understanding.

Findings

Established the waveform-estimation Holevo Cramér-Rao Bound.

Demonstrated how to attain the bound with nonstationary measurements.

Proposed a method to improve signal-to-noise ratio by a factor of √2.

Abstract

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation Quantum Cram\'er-Rao Bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cram\'er-Rao Bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for post-merger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal's power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of $\sqrt2$ using this nonstationary measurement.