# Signaling and Scrambling with Strongly Long-Range Interactions

## TL;DR

This paper establishes new Lieb-Robinson-type bounds for strongly long-range quantum systems, providing insights into the limits of information signaling and scrambling, which are crucial for understanding quantum dynamics in non-local systems.

## Contribution

It introduces two novel bounds on signaling and scrambling times in long-range interacting quantum systems, advancing theoretical understanding of their dynamics.

## Key findings

- Bounds are tight for systems mappable to free-particle Hamiltonians with long-range hopping.
- Lower bounds on signaling time are established for all  systems with  < .
- Results suggest a pathway to proving the fast scrambling conjecture.

## Abstract

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional lattice for $\alpha\le D$---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\alpha\le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all $\alpha < D$. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.