Metrological quantum-to-classical crossover in the volume of a noisy quasiperiodic lattice
Localization-delocalization transitions have recently been proposed for building a class of efficient quantum many-body critical sensors. This work scrutinizes metrological performances of such devices by focusing on the Aubry-Andr\'e-Harper model that supports a localization-delocalization transition at finite strength of the onsite potential. We identify a metrological quantum-to-classical crossover driven by the interplay between noise and system size, whereby quantum-enhanced scaling of the quantum Fisher information persists only up to a finite, noise-dependent characteristic system-size. We first consider thermal noise and show that, at and near the localization-delocalization transition, the quantum Fisher information exhibits quantum-enhanced scaling for small systems but the system is stripped of this advantage beyond the characteristic crossover length. The crossover length decreases with increasing temperature. We then consider imperfections in the lattice hopping strengths and find a qualitatively similar crossover. There, the quantum-enhanced regime, identified with super-extensive scaling, gives way to an extensive scaling-a classical-limited weaker form-at sufficiently large system sizes. Thus, distinct noise mechanisms lead to a common limitation on the scalability of quantum-enhanced sensing: increasing the probe size beyond a noise-dependent limit can destroy the metrological quantum advantage.