  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 resources $N$ in the estimation process.
Although previous experiments demonstrated precision scaling approaching
Heisenberg-limited performances, reaching such 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.
