Parallel-mode-channel approach to multimode Gaussian state estimation

Abstract

The imaging process and its corresponding state estimation are treated as parallel mode channels and two estimation subproblems, respectively. In the two subproblems, the displacement vector and covariance matrix of the object field are estimated independently from the measured ones of the aperture field by minimizing their respective cost functions defined quantum mechanically. The measurement scheme is also briefly discussed. As an application, the location estimation of a point feature of a disk object is studied analytically and numerically. The results show that the estimation that uses only the displacement vector does not enhance the resolution of the amplitude image to a large extent. On the contrary, the quantum Cram\'er-Rao bound of spatial resolution can be pushed down toward the uncertainty relation. Furthermore, the high quantum fidelities verify the effectiveness of the estimation and the broad applicability to arbitrary multimode Gaussian states.