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  • Open Access

Quantum Advantage for Sensing Properties of Classical Fields

Jordan Cotler1,2,*, Daine L. Danielson1,3,4,†, and Ishaan Kannan1,2,‡

  • *Contact author: jcotler@fas.harvard.edu
  • †Contact author: daine@mit.edu
  • ‡Contact author: ishaan_kannan@g.harvard.edu
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Phys. Rev. X 16, 041025 – Published 23 October, 2026

DOI: https://doi.org/10.1103/6ps1-mw9l

Abstract

Modern precision experiments often probe unknown classical fields with bosonic sensors in quantum-noise-limited regimes where vacuum fluctuations limit conventional readout. We introduce quantum signal learning, a sensing framework that extends metrology to a broader property-learning setting, and propose a quantum-enhanced protocol that simultaneously estimates many properties of a classical signal with shot noise suppressed below the vacuum level. Our scheme requires only two-mode squeezing, passive optics, and static homodyne measurements, and enables post hoc classical estimation of many properties from the same experimental dataset. We prove that our protocol enables a quantum speedup for common classical sensing tasks, including measuring electromagnetic correlations, real-time feedback control of interferometric cavities, and Fourier-domain matched filtering. To establish these separations, we introduce an optimal-transport conditioning method and show both worst-case exponential separations from all entanglement-free strategies and practical speedups over homodyne and heterodyne baselines. We further show that when squeezing is treated as a resource, a protocol with squeezed light can sense a structured classical background exponentially faster than any coherent classical probe.

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Popular Summary

The world’s best sensors—from gravitational-wave observatories to precision radar—detect signals so faint that the dominant noise comes from electromagnetic fluctuations of empty space. Modern experiments now face a trade-off: They can record everything about an incoming signal but pay a quantum noise penalty, or use quantum light to measure one feature with exquisite precision while remaining blind to the rest. We introduce a protocol called Bell quantum signal learning (QSL) that dissolves this trade-off. Bell QSL uses quantum entanglement to push noise below the vacuum level while collecting data that can be used to simultaneously estimate a wide variety of physical properties. In some cases, the resulting speedup exponentially outperforms any strategy for sensing without quantum entanglement. Built from components standard in today’s laboratories, Bell QSL could sharpen searches for gravitational waves, dark matter, and faint electromagnetic signals.

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Outline

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Phys. Rev. X 16, 041025– Published 23 October, 2026
  • Received 27 March 2026
  • Revised 21 June 2026
  • Accepted 14 August 2026
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