Characterizing quantum states of light using ghost imaging

Ghost imaging can be implemented with illumination light with pronounced quantum characters. In this work, we address the inverse problem of ghost imaging, i.e., the tomography of the quantum states of illumination light based on ghost imaging. We showcase the characterization of multimode Gaussian state light represented by its covariance matrix. With the information of spatial modes, we reconstruct the quantum states of light using the variation of SNR of the ghost images formed by the input light under a given set of optical operations. We demonstrate that ghost imaging can also be used to characterize the non-Gaussian light by its deviation from Gaussian states, which can serve as a criterion for the non-Gaussianity of the input light. The spatial resolving power of the proposed method can be advantageous for quantum information applications involving structured light, such as multiplexing with spatial modes.