Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a function of the employed resourcesN in the estimation process. Although previous experiments demonstrated precision scaling approaching Heisenberg-limited performances, reaching such a regime for a wide range of N remains hard to accomplish. Here, we show a method which suitably allocates the available resources reaching Heisenberg scaling without any prior information on the parameter. We demonstrate experimentally such an advantage in measuring a rotation angle. We quantitatively verify Heisenberg scaling for a considerable range of N by using single-photon states with high-order orbital angular momentum, achieving an error reduction greater than 10 dB below the standard quantum limit. Such results can be applied to different scenarios, opening the way to the optimization of resources in quantum sensing.
V. Cimini, E. Polino, F. Belliardo, F. Hoch, B. Piccirillo, N. Spagnolo, V. Giovannetti and F. Sciarrino. Non-asymptotic Heisenberg scaling: experimental metrology for a wide resources range [arXiv:2110.02908]