Anthony Chen Chi-Fang, Lucas Andrew, Yin Chao
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, United States of America.
Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, United States of America.
Rep Prog Phys. 2023 Sep 29;86(11). doi: 10.1088/1361-6633/acfaae.
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.
我们回顾了多体系统中量子信息处理的数学速度限制。1972年利布-罗宾逊定理得到证明后，在过去二十年中，其在应用于其他问题方面取得了重大进展，比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，甚至是有能隙系统基态的性质。此外，利布-罗宾逊界已通过非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中的速度限制，甚至用于证明在具有全对全相互作用的量子引力卡通模型中出现的局域性概念。我们概述了已取得的进展，突出了最有前景的结果和技术，并讨论了一些仍然悬而未决的核心问题。为帮助该领域的新手跟上进度，我们给出了该领域最基本结果的自包含证明。
