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/N2). 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(N2). 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/N2).
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BibTeX
@misc{yunoki2026heisenberg,
title = {{Heisenberg Scaling in Many-Body Kinetic Uncertainty Relation via Quantum Feedback}},
author = {Hayato Yunoki and Yoshihiko Hasegawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.12264},
eprint = {2607.12264},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12264},
}
RIS
TY - UNPB
TI - Heisenberg Scaling in Many-Body Kinetic Uncertainty Relation via Quantum Feedback
AU - Hayato Yunoki
AU - Yoshihiko Hasegawa
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2607.12264
UR - https://arxiv.org/abs/2607.12264
AB - 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).
ER -