Since its discovery, quantum entanglement has challenged some of the best established views of the world: locality and reality. Quantum technologies promise to revolutionize computation, communication, metrology and imaging. Here we review conceptual and experimental advances in complex entangled systems involving many multilevel quantum particles. We provide an overview of the latest technological developments in the generation and manipulation of high-dimensionally entangled photonic systems encoded in various discrete degrees of freedom such as path, transverse spatial modes or time–frequency bins. This overview should help to transfer various physical principles for the generation and manipulation from one degree of freedom to another and thus inspire new technical developments. We also show how purely academic questions and curiosity led to new technological applications. Fundamental research provides the necessary knowledge for upcoming technologies, such as a prospective quantum internet or the quantum teleportation of all information stored in a quantum system. Finally, we discuss some important problems in the area of high-dimensional entanglement and give a brief outlook on possible future developments.

自从发现以来，量子纠缠就挑战了世界上一些公认的观点：局部性和现实性。量子技术有望彻底改变计算，通信，计量和成像技术。在这里，我们回顾了涉及许多多级量子粒子的复杂纠缠系统的概念和实验进展。我们概述了以各种离散的自由度编码的高维纠缠光子系统的生成和操作的最新技术进展，这些自由度例如路径，横向空间模式或时频箱。此概述应有助于将用于生成和操纵的各种物理原理从一种自由度转移到另一种自由度，从而激发新的技术发展。我们还展示了纯粹的学术问题和好奇心如何导致了新技术的应用。基础研究为即将到来的技术提供了必要的知识，例如预期的量子互联网或量子系统中存储的所有信息的量子隐形传态。最后，我们讨论了高维纠缠领域中的一些重要问题，并对可能的未来发展作了简要展望。