Metrology of quantum imaging schemes
We compare the performance of quantum imaging schemes based on spatially correlated photon pairs by formulating them as quantum multiparameter estimation problems, in which the object is characterized by transmission coefficients associated with different spatial modes. Our work focuses on standard quantum imaging techniques such as ghost imaging, two-photon imaging, and imaging with undetected photons. Specifically, we compute the quantum Fisher information matrices and show that they are saturated by Fisher information matrices corresponding to measurements in the object-mode basis, which generalize the common detection schemes employed in each imaging configuration. We find that ghost imaging and two-photon imaging generally provide higher precision for transmission estimation than imaging with undetected photons, but the latter is the only one that naturally does not couple transmission estimation across different spatial modes. These results identify which imaging protocols are best suited for specific tasks and provide practical guidelines for the design and optimization of quantum sensing technologies based on spatial correlations.