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Stochastic Waveform Estimation at the Fundamental Quantum Limit

James W. Gardner1,2,*, Tuvia Gefen3,†, Simon A. Haine4, Joseph J. Hope4, John Preskill2,3, Yanbei Chen2, and Lee McCuller3,5

  • *Contact author: james.gardner@anu.edu.au
  • †Contact author: tgefen@caltech.edu
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PRX Quantum 6, 030311 – Published 22 July, 2025

DOI: https://doi.org/10.1103/h91r-4ws9

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 Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

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Popular Summary

Many current searches for new fundamental physics aim to sense the power in a weak, randomly fluctuating signal. Examples of such experiments include probes for quantum gravity, stochastic gravitational waves, and ultralight dark matter. Accelerating these searches for fundamental physics is crucial to testing our theories of nature. However, these signals are so weak that our searches are limited by the quantum nature of our precision sensors. How to best overcome this quantum noise using different strategies is not known. In particular, conventional Gaussian schemes that are optimal for sensing deterministic signals perform poorly for sensing these stochastic signals.

We find the ultimate sensitivity limit of a linear device to stochastic signals. We identify the best strategy for preparing particular quantum states and performing particular quantum measurements. In the presence of decoherence, relevant for any actual experiment, we show that the optimal protocol is highly non-Gaussian. This represents a radical departure from the deterministic sensing case and the conventional protocols that are unable to sense the weakest stochastic signals. Instead, one optimal non-Gaussian strategy is to prepare the device in a Gottesman-Kitaev-Preskill grid state, famous in the field of quantum error correction. These non-Gaussian states are also required if we want to simultaneously sense both the mean and variance of a signal.

On the experimental side, we provide a blueprint for implementing these techniques in state-of-the-art quantum platforms. On the theoretical side, for future work, studying the estimation of non-Gaussian and finite coherence time signals is particularly promising.

Article Text

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PRX Quantum 6, 030311– Published 22 July, 2025
  • Received 1 May 2024
  • Revised 9 May 2025
  • Accepted 12 June 2025
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