Super-resolution of partially coherent bosonic sources

We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable both in the presence of nuisance parameters as well as when some of the parameters are assumed known. Nuisance parameters restrict super-resolution to balanced sources, whereas for known parameters super-resolution persists over a broader range of relative intensities and is lost only for perfectly correlated sources, i.e., $\gamma=1$. The achievable precision is governed primarily by interference-induced photon statistics and depends strongly on the degree of coherence. In the sub-Rayleigh regime, the imaging problem reduces to an effective two-dimensional Hilbert space description, provided a consistent reference position is used, with all parameters encoded in a Bloch vector representation. Finally, indirect estimation schemes based on the purity of the image-plane state are generally suboptimal for all non-zero coherence and become valid only in the incoherent limit.