The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a possible reconstruction of the underlying process. The tomography is typically performed by processing an overcomplete set of measurements and extracting the process matrix from maximum-likelihood estimation. Here, we introduce Fourier Quantum Process Tomography, a technique which requires a reduced number of measurements, and benchmark its performance against the standard maximum-likelihood approach. Fourier Quantum Process Tomography is based on measuring probability distributions in two conjugate spaces for different state preparations and projections. Exploiting the concept of phase retrieval, our scheme achieves a complete and robust characterization of the setup by processing a near-minimal set of measurements. We experimentally test the technique on different space-dependent polarization transformations, reporting average fidelities higher than 90% and significant computational advantage.

量子器件的表征是量子实验发展的关键一步。这是通过量子过程断层扫描来实现的，它结合了不同投影测量的结果，以提供潜在过程的可能重建。断层扫描通常是通过处理一组超完备的测量值并从最大似然估计中提取过程矩阵来执行的。在这里，我们介绍傅里叶量子过程断层扫描，这是一种需要减少测量次数的技术，并根据标准最大似然方法对其性能进行基准测试。傅里叶量子过程断层扫描基于测量不同状态准备和投影的两个共轭空间中的概率分布。利用相位检索的概念，我们的方案通过处理近乎最小的测量集来实现对设置的完整且稳健的表征。我们在不同的空间相关偏振变换上实验测试了该技术，报告平均保真度高于 90%，并且具有显着的计算优势。