On Propagation of Information in Quantum Mechanics and Maximal Velocity Bounds

TL;DR

This paper establishes uniform bounds on the speed of quantum information propagation in few-body quantum mechanics, extending Lieb-Robinson bounds to a broader class of dispersion relations and introducing a new proof approach.

Contribution

It provides a new method for proving maximal speed bounds in quantum systems and extends Lieb-Robinson bounds to more general dispersion relations.

Findings

Established uniform bounds on quantum information speed

Extended Lieb-Robinson bounds to wider dispersion relations

Introduced a novel proof approach for maximal speed bounds

Abstract

We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for states and observables with exponential error bounds. Our results imply, in particular, a fbQM version of the Lieb-Robinson bound, which is known to have wide applications in quantum information sciences. We propose a novel approach to proving maximal speed bounds.