Nonlinear Enhancement of Measurement Precision via a Hybrid Quantum Switch

Quantum metrology promises measurement precision beyond the classical limit by using suitably tailored quantum states and detection strategies. However, scaling up this advantage is experimentally challenging, due to the difficulty of generating high-quality large-scale probes. Here, we build a photonic setup that achieves enhanced precision scaling by manipulating the probe’s dynamics through operations performed in a coherently controlled order. Our setup applies an unknown rotation and a known orbital angular momentum increase in a coherently controlled order, in a way that reproduces a hybrid quantum SWITCH involving gates generated by both discrete and continuous variables. The unknown rotation angle θ is measured with precision scaling as 1/4ml when a photon undergoes a rotation of 2mθ and an angular momentum shift of 2lℏ. With a practical enhancement factor as high as 2317, the ultimate precision in our experiment is 0.0105′′ when using 7.16 × 107 photons, corresponding to a normalized precision of ≈ 10−4rad per photon. No photon interaction occurs in our experiment, and the precision enhancement consumes only a linearly increasing amount of physical resources while achieving a nonlinear scaling of the precision.