Bayesian frequency estimation at the fundamental quantum limit

• URL: http://arxiv.org/abs/2507.02811v2
• Date: Tue, 29 Jul 2025 01:47:12 GMT
• Title: Bayesian frequency estimation at the fundamental quantum limit
• Authors: James W. Gardner, Tuvia Gefen, Ethan Payne, Su Direkci, Sander M. Vermeulen, Simon A. Haine, Joseph J. Hope, Lee McCuller, Yanbei Chen,
• Abstract summary: We show that a quadrature measurement can be beaten by a coherent protocol of projecting onto the "quantum whitened" possible quantum states.<n> Quantum whitening is a covariant measurement, and we examine it analytically in the wide-prior limit and numerically for finite-width priors.
• Score: 8.32805126711427
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Searching for a weak signal at an unknown frequency is a canonical task in experiments probing fundamental physics such as gravitational-wave observatories and ultra-light dark matter haloscopes. These state-of-the-art sensors are limited by quantum noise arising from the fundamental uncertainty about the state of the device. Classically, frequency estimation suffers from a threshold effect in the signal-to-noise ratio such that weak signals are extremely hard to localise in frequency. We show that this phenomenon persists at the fundamental quantum limit but that the classical approach, a quadrature measurement, can nevertheless be beaten by a coherent protocol of projecting onto the "quantum whitened" possible quantum states. Quantum whitening is a covariant measurement, and we examine it analytically in the wide-prior limit and numerically for finite-width priors. Beyond accelerating searches for unknown frequencies, quantum whitening may be used generally to sense the parameter of a unitary encoding given no prior information about the parameter.

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