Experimental broad range Heisenberg scaling estimation in the non-asymptotic regime*

Quantum Metrology represents one of the most promising applications of quantum technologies, with the aim of using quantum resources to improve the sensitivity of quantum sensors. Here, it is crucial to reach quantum-enhanced estimation for a large resources range, a task that is still a fundamental open problem. Indeed, the states and the techniques which are commonly used to achieve such an advantage are usually too sensitive to losses. Here, we experimentally demonstrate a novel approach which allows to achieve a sub-standard-quantum-limit precision in the measurement of a rotation angle, reaching the Heisenberg scaling, for an unexplored wider range of dedicated resources. The key element to enlarge the enhanced scaling range is to properly allocate the available resources during the estimation process. Such a requirement is fulfilled by exploiting the orbital angular momentum of single photon states, scaling its value only when required by the estimation protocol. To develop such a strategy, we have implemented a new fully automatized platform composed of a series of q-plates with an increasing topological charge arranged in a cascade configuration. Such setup gives us the possibility to increase efficiently the number of total resources during the estimation procedure.