Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions

TitleFast State Transfer and Entanglement Renormalization Using Long-Range Interactions
Publication TypeJournal Article
Year of Publication2017
AuthorsEldredge, Z, Gong, Z-X, Moosavian, AHamed, Foss-Feig, M, Gorshkov, AV
JournalPhysical Review Letters
Date Published2017/10/25

In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with strength bounded by 1/rα. If α<d, the state transfer time is asymptotically independent of L; if α=d, the time is logarithmic in distance L; if d<α<d+1, transfer occurs in time proportional to Lαd; and if αd+1, it occurs in time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is L, then it can be created in time that scales with L identically to state transfer up to multiplicative logarithmic corrections.