Quantum resources enhance parameter estimation sensitivity beyond the standard quantum limit (SQL), potentially achieving Heisenberg scaling (∝1/N). While previous experiments approached Heisenberg-limited performance, achieving this across a wide range of resources (N) remained challenging. This paper presents a method for optimal resource allocation to attain Heisenberg scaling without prior parameter knowledge. Experimental demonstration using high-order orbital angular momentum (OAM) single-photon states shows sub-SQL performance for a substantial N range (O(30,000)), with variance reduction >10 dB below the SQL. These findings are applicable to various scenarios, optimizing resource use in quantum sensing.

Valeria Cimini, Emanuele Polino, Federico Belliardo, Francesco Hoch, Bruno Piccirillo, Nicolò Spagnolo, Vittorio Giovannetti, Fabio Sciarrino