We present a method to reconstruct pure spatial qudits of arbitrary dimension $d$, 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 with $d$ slits, and a known background is added to provide 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 dimension $d$. We tested the method experimentally, for reconstructing states of dimension $d=6$ 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.

中文翻译：

---

使用点衍射干涉法测定空间量子态

我们提出了一种重建任意维度 $d$ 的纯空间量子的方法，该方法基于点衍射干涉仪。在所提出的方案中，一旦量子态通过具有 d 条狭缝的孔径发送，就会在光子场的离散横向位置中编码，并添加已知背景以提供相位参考。为了表征这些光子量子态，通过相移技术重建了完整的相位波前。结合多像素检测器，采集可以并行化，并且只需要四个干涉图来重建任何纯量子，独立于维度 $d$。我们通过实验测试了该方法，用于重建随机选择的维度 $d=6$ 的状态。获得了 0.95 美元的平均保真度值。此外，我们开发了一种实验方案，可以估计传播时影响波前的相位像差，从而改进量子状态估计。在这方面，我们提出了一个原理验证演示，展示了在自由空间通信中纠正湍流影响的可能性，恢复与无湍流传播相当的平均保真度值。