Quantum super-resolution for imaging two pointlike entangled photon sources

We investigate the resolution for imaging two pointlike entangled sources by using the method of the moments and the spatial-mode demultiplexing (SPADE), where the pointlike entangled sources can be generated by injecting single-mode sources with arbitrary quantum statistics distribution into an optical parametric amplifier (OPA). We demonstrate that the separation estimation sensitivity is mainly determined by the photon distribution in each detected modes and it can be enhanced by either increasing the squeezed parameter of the OPA or eliminating the relative phase difference of the entangle sources. Furthermore, in the limiting case of infinitely small source separation, the usage of entangled sources can have better resolution than those using incoherent and coherent sources. The results here can find important applications for the quantum super-resolution imaging and quantum metrology.