Heisenberg Scaling in Many-Body Kinetic Uncertainty Relation via Quantum Feedback

Abstract:Kinetic uncertainty relations impose a fundamental constraint on counting precision by requiring large dynamical activity to suppress fluctuations. For $N$ independent constituents, the activity is additive and scales as $O(N)$, so the corresponding precision bound improves only as $O(1/N)$. A central question is whether many-body quantum systems can instead achieve Heisenberg scaling, with relative variance suppressed as $O(1/N^{2})$. Such scaling could enable substantially enhanced precision in quantum devices, including quantum clocks. Superradiance appears to provide a natural route because its collective emission activity can scale as $O(N^2)$. We show, however, that superradiance alone fails to achieve Heisenberg scaling because this enhanced activity is transient. We then demonstrate that jump-conditioned quantum feedback stabilizes the superradiant high-activity regime and converts this collective enhancement into Heisenberg scaling. We establish this mechanism analytically using a many-body kinetic uncertainty relation and mean-field analysis, and demonstrate through quantum-trajectory simulations that the actual relative counting fluctuation scales as $O(1/N^{2})$.

arXiv:2607.12264 [quant-ph]

(or arXiv:2607.12264v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.12264 Focus to learn more arXiv-issued DOI via DataCite

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