Determination of spatial quantum states by using Point Diffraction Interferometry

We present a method to reconstruct pure spatial qudits of arbitrary dimensiond, which is based on a point diffraction interferometer. In the proposed scheme, the quantum states are codified in the discretized transverse position of a photon field, once they are sent through an aperture consisting indrectangular regions, with an extra region that provides a phase reference. To characterize these photonic quantum states, the complete phase wavefront is reconstructed through a phase-shifting technique. Combined with a multipixel detector, the acquisition can be parallelized, and only four interferograms are required to reconstruct any pure qudit, independently of the dimensiond. We tested the method experimentally, for reconstructing states of dimensiond = 6 randomly chosen. A mean fidelity values of 0.95 is obtained. Additionally, we develop an experimental scheme that allows to estimate phase aberrations affecting the wavefront upon propagation, and thus improve the quantum state estimation. In that regard, we present a proof-of-principle demonstration that shows the possibility to correct the influence of turbulence in a free-space communication, recovering mean fidelity values comparable to the propagation free of turbulence.