Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions

Understand

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 $1/r^\alpha$.
• If $\alpha < d$, the state transfer time is asymptotically independent of $L$; if $\alpha = d$, the time is logarithmic in distance $L$; if $d < \alpha < d+1$, transfer occurs in time proportional to $L^{\alpha - d}$; and if $\alpha \geq d + 1$, it occurs in time proportional to $L$.