Nanoradian-scale precision in light rotation measurement via indefinite quantum dynamics.

The manipulation and metrology of light beams are pivotal for optical science and applications. In particular, achieving ultrahigh precision in the measurement of light beam rotations has been a long-standing challenge. Instead of using quantum probes like entangled photons, we address this challenge by incorporating a quantum strategy called "indefinite time direction" into the parameterizing process of quantum parameter estimation. Leveraging this quantum property of the parameterizing dynamics allows us to maximize the utilization of orbital angular momentum resources for measuring ultrasmall angular rotations of beam profile. Notably, a nanoradian-scale precision of light rotation measurement is lastly achieved in the experiment, which is the highest precision by far to our best knowledge. Furthermore, this scheme holds promise in various optical applications due to the diverse range of manipulable resources offered by photons.