Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2021 Oct 15;127(16):160401. doi: 10.1103/PhysRevLett.127.160401.
The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/r^{α} at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least r^{min{1,α-2d}} to propagate a distance r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.
李-罗宾逊定理指出，在具有最近邻相互作用的晶格上的量子系统中，信息以有限的速度传播。那么，在幂律相互作用的量子系统中，信息传播的速度限制是多少？其中，相互作用随着距离 r 呈 1/r^{α}衰减。在这里，我们为所有指数 α>2d 和所有空间维度 d 给出了这个问题的明确答案。大致来说，信息传播距离 r 需要至少 r^{min{1,α-2d}}}的时间。由于最近的状态转移协议达到了这个边界，我们的工作结束了长达数十年的对具有幂律相互作用的量子信息动力学的最优李-罗宾逊边界的探索。
