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.

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