Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors

Abstract:Quantum metrology promises sensitivity beyond classical strategies, yet it remains unsettled how quantum-enabled precision should scale with physical resources and how to interpret quantum advantage. We provide a physically grounded resource accounting that clarifies the true Heisenberg limit and resolves apparent super-Heisenberg paradoxes. We demonstrate that the Heisenberg limit is best viewed as an information-theoretic manifestation of the quantum speed limit. We illustrate these ideas with a simple, super-resolving phase-estimation protocol based on Rabi oscillations in two-level atoms driven on an $m$-photon resonance. In this setting, the phase error scales as $n^{-m/2}$, where $n$ is the average photon number. Recasting metrological sensitivity through quantum dynamical speed limits yields operational bounds that reconcile such super-resolution strategies with the standard Heisenberg interpretation and identify the relevant resources in the norm of the generator. We also revisit the common attribution of the NOON state's $1/n$ scaling to quantum entanglement. We show that such an attribution is not generic and the Heisenberg $1/n$ scaling does not, by itself, certify entanglement as the enabling resource.

arXiv:2607.23573 [quant-ph]

(or arXiv:2607.23573v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.23573 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.3390/e28080836 Focus to learn more DOI(s) linking to related resources

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