# Finite speed of quantum scrambling with long range interactions

## TL;DR

This paper proves that quantum information scrambling occurs at a finite speed in one-dimensional systems with long-range interactions, extending understanding beyond short-range models and impacting quantum simulation and decoherence bounds.

## Contribution

It establishes a finite scrambling speed for long-range interactions in 1D systems, improving previous bounds and applicable to real quantum simulators with dipolar interactions.

## Key findings

- Scrambling speed remains finite for large interaction decay exponents.
- Improved bounds compared to previous theoretical results.
- Relevance to quantum simulators with dipolar interactions.

## Abstract

In a locally interacting many-body system, two isolated qubits, separated by a large distance $r$, become correlated and entangled with each other at a time $t \ge r/v$. This finite speed $v$ of quantum information scrambling limits quantum information processing, thermalization and even equilibrium correlations. Yet most experimental systems contain long range power law interactions -- qubits separated by $r$ have potential energy $V(r)\propto r^{-\alpha}$. Examples include the long range Coulomb interactions in plasma ($\alpha=1$) and dipolar interactions between spins ($\alpha=3$). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large $\alpha$. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors.