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arXiv:2601.01820

Heisenberg scaling in optical magnetometry with measurement-induced correlations as a quantum resource

Georg Engelhardt, Ming Li, Xingchang Wang, JunYan Luo, J. F. Chen

quant-phSubmitted Jan 5, 2026• Announced Jan 6, 2026• 0 citations• Revised Jul 24, 2026 (v2)
v1 · Jan 5, 2026v2 · Jul 24, 2026
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Abstract

Theoretical proposals to reach the Heisenberg scaling of the measurement precision typically require carefully engineered interactions or initial entanglement. In studying optical magnetometry, we show that the continuous collective measurement process itself can generate the necessary many-body quantum correlations to achieve the elusive Heisenberg scaling of the quantum Fisher information in a dissipative, steady-state system without direct inter-atomic interactions. By contrasting a correlation-neglecting but otherwise consistent semiclassical model, which can violate the quantum Cramér-Rao bound (QCRB) by several orders of magnitude, with a collective quantum model, we isolate measurement-induced correlations as the essential mechanism. The violation of the QCRB serves thereby as a fundamental sanity check for semiclassical spectroscopic theories. This work reveals measurement-induced correlations as a widely unexplored quantum resource for quantum-enhanced sensing, establishes a new paradigm for achieving Heisenberg scaling in open quantum systems, and provides a direct path to test the foundations of quantum mechanics using macroscopic atom ensembles.

Comments
28 pages including appendices; 5 figures; comments are welcome

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Theoretical proposals to reach the Heisenberg scaling of the measurement precision typically require carefully engineered interactions or initial entanglement. In studying optical magnetometry, we show that the continuous collective measurement process itself can generate the necessary many-body quantum correlations to achieve the elusive Heisenberg scaling of the quantum Fisher information in a dissipative, steady-state system without direct inter-atomic interactions. By contrasting a correlation-neglecting but otherwise consistent semiclassical model, which can violate the quantum Cramér-Rao bound (QCRB) by several orders of magnitude, with a collective quantum model, we isolate measurement-induced correlations as the essential mechanism. The violation of the QCRB serves thereby as a fundamental sanity check for semiclassical spectroscopic theories. This work reveals measurement-induced correlations as a widely unexplored quantum resource for quantum-enhanced sensing, establishes a new paradigm for achieving Heisenberg scaling in open quantum systems, and provides a direct path to test the foundations of quantum mechanics using macroscopic atom ensembles.
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The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.
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Free-electron quantum optics has recently emerged as a promising platform for coherent electron-light interactions, yet its potential for quantum-enhanced metrology remains largely unexplored. Here, we investigate the fundamental precision limit of coupling-strength estimation in multi-electron photon-induced near-field electron microscopy (PINEM), demonstrating that the quantum Fisher information scales quadratically with electron number. We then propose an experimentally accessible scheme combining squeezed-light probing and optical homodyne detection that attains Heisenberg scaling with respect to electron number, provided the electrons exhibit nonzero inter-electron coherence, while surpassing conventional PINEM sensing in photon-number enhancement as well. We further analyze the effect of imperfect electron preparation, showing that electron phase noise is converted into a fluctuating optical displacement and eventually limits the precision. To overcome this limitation, an auxiliary optical mode coupled to the same electron ensemble measures the displacement noise in the signal mode, allowing its conditional suppression and recovery of the Heisenberg scaling. Our work establishes multi-electron coherence as a resource for free-electron quantum metrology and opens the route to precision measurements of nanoscale electron-light interactions.