Maximal Speed of Propagation in Open Quantum Systems

TL;DR

This paper establishes a maximal speed limit for how quickly information and perturbations can propagate in open quantum systems described by Lindblad equations, defining a quantum light cone with polynomial error bounds.

Contribution

It provides the first rigorous bound on the maximal propagation speed in Markovian open quantum systems, extending Lieb-Robinson type bounds to dissipative dynamics.

Findings

States remain within a light cone up to polynomial errors.

Bound on the slope of the light cone, i.e., maximal propagation speed.

Upper bound on the speed of local perturbations in stationary states.

Abstract

We prove a maximal velocity bound for the dynamics of Markovian open quantum systems. The dynamics are described by one-parameter semi-groups of quantum channels satisfying the von Neumann-Lindblad equation. Our result says that dynamically evolving states are contained inside a suitable light cone up to polynomial errors. We also give a bound on the slope of the light cone, i.e., the maximal propagation speed. The result implies an upper bound on the speed of propagation of local perturbations of stationary states in open quantum systems.