In the past few years, physicists and engineers have demonstrated the possibility of utilizing multiple degrees of freedom of the photon to perform information processing tasks for a wide variety of applications. Furthermore, complex states of light offer the possibility of encoding and processing many bits of information in a single photon. However, the challenges involved in the process of extracting large amounts of information, encoded in photonic states, impose practical limitations to realistic quantum technologies. Here, we demonstrate characterization of quantum correlated photon pairs in the spatial and spectral degrees of freedom. Our technique utilizes a series of random projective measurements in the spatial basis that do not perturb the spectral properties of the photon. The sparsity in the spatial properties of downconverted photons allows us to exploit the potential of compressive sensing to reduce the number of measurements to reconstruct spatial and spectral properties of correlated photon pairs at telecom wavelength. We demonstrate characterization of a photonic state with $12\times {10}^9$ dimensions using only 20% of the measurements with respect to the conventional raster scan technique. Our characterization technique opens the possibility of increasing and exploiting the complexity and dimensionality of quantum protocols that utilize multiple degrees of freedom of light with high efficiency.

中文翻译：

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在空间和光谱自由度中对电信光子对的压缩表征

在过去的几年中，物理学家和工程师证明了利用光子的多个自由度来执行各种应用程序的信息处理任务的可能性。此外，复杂的光状态提供了在单个光子中编码和处理许多位信息的可能性。然而，以光子态编码的提取大量信息的过程中所涉及的挑战对现实的量子技术施加了实际限制。在这里，我们展示了空间和光谱自由度中的量子相关光子对的表征。我们的技术在空间基础上利用了一系列随机投影测量，这些测量不干扰光子的光谱特性。下转换光子空间特性的稀疏性使我们能够利用压缩感测的潜力来减少测量次数，以重建电信波长下相关光子对的空间和光谱特性。我们展示了一个光子状态的表征$12\times {10}^9$相对于传统的光栅扫描技术，仅使用测量值的20％来确定尺寸。我们的表征技术开辟了增加和利用量子协议的复杂性和维度的可能性，量子协议以高效率利用光的多个自由度。