Fundamental Quantum Limit to Waveform Estimation

TL;DR

This paper establishes a fundamental quantum limit, via the quantum Cramér-Rao bound, on the accuracy of estimating time-varying signals with quantum sensors, impacting fields like gravitational-wave detection and magnetometry.

Contribution

It derives a universal quantum limit for waveform estimation errors and demonstrates how quantum noise cancellation and smoothing can reach this bound.

Findings

Quantum Cramér-Rao bound sets a fundamental limit on waveform estimation.

The bound manifests as a spectral uncertainty principle for force sensing.

Quantum noise cancellation and smoothing enable reaching the quantum limit.

Abstract

We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and atomic magnetometers. We apply the QCRB to the problem of force estimation via continuous monitoring of the position of a harmonic oscillator, in which case the QCRB takes the form of a spectral uncertainty principle. The bound on the force-estimation error can be achieved by implementing quantum noise cancellation in the experimental setup and applying smoothing to the observations.