On propagation of information in quantum many-body systems

TL;DR

This paper establishes bounds on the speed of information propagation in quantum many-body systems, demonstrating a light-cone structure that applies even with long-range interactions, crucial for understanding quantum dynamics.

Contribution

It introduces a maximal velocity bound for quantum systems, extending Lieb-Robinson bounds to long-range interactions and providing a framework for quantum information propagation analysis.

Findings

Proves bounds on quantum messaging times

Establishes light-cone approximation for dynamics

Extends bounds to systems with long-range interactions

Abstract

We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the many-body evolution stays, up to small leaking probability tails, within a light cone of the support of the initial conditions. This estimate is used to prove the light-cone approximation of dynamics and Lieb-Robinson-type bound, which in turn yield the results above. Our conditions cover long-range interactions. The main results of this paper as well as some key steps of the proofs were first presented in [36].