We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb–Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb–Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field’s most essential results.

中文翻译：

---

多体量子动力学中的速度限制和局域性


我们回顾了多体系统中量子信息处理的数学速度限制。自 1972 年证明了利布-罗宾逊定理之后，过去二十年里它在其他问题上的应用取得了实质性发展，例如量子系统在经典或量子计算机上的可模拟性、纠缠的产生，甚至是量子力学的性质。有隙系统的基态。此外，利布-罗宾逊界限已经以不平凡的方式得到扩展，以证明具有幂律相互作用或相互作用玻色子的系统的速度限制，甚至证明了量子引力卡通模型中出现的局域性概念。所有互动。我们概述了已经发生的进展，强调了最有希望的结果和技术，并讨论了一些仍然悬而未决的核心悬而未决的问题。为了帮助新手快速了解该领域，我们提供了该领域最重要结果的独立证明。