Multi-parameter two-photon polarimetry at the quantum limit

Photonic quantum metrology has demonstrated advantages in precision and resource efficiency for a wide range of applications, with several schemes approaching the fundamental quantum Cram\'er-Rao precision bound (QCRB). However, the intrinsic incompatibility of quantum measurements represents a hurdle in extending these advantages to the simultaneous estimation of multiple parameters. In this paper, we present an experimental protocol approaching the QCRB simultaneously in two polarisation parameters, across a wide range of the parameter space, with as few as $\sim 200$ photon pairs, offering advantages for polarimetric sensing for dim sources such as in X-ray astronomy or photosensitive samples.