Limits to velocity of signal propagation in many-body systems: a quantum-information perspective

TL;DR

This paper introduces a quantum information-based method to determine the Lieb-Robinson bound in many-body systems using local measurements, simplifying the process of estimating signal propagation limits.

Contribution

It presents an operational approach to estimate the Lieb-Robinson bound from local qubit measurements, replacing complex correlation function measurements.

Findings

Derived the upper limit to signal speed in XY spin chain.

Demonstrated the method's effectiveness in complex many-body systems.

Provided a practical recipe for experimental estimation of information propagation limits.

Abstract

The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of correlation function connecting two distant subsystems. Here we employ the techniques of quantum information to demonstrate that the LRB can be determined from local measurements performed on a single qubit that is connected to a many-body system. This formulation provides an operational recipe for estimating the LRB in complex systems, replacing the measurement of the correlation function with simple single-particle manipulations. We demonstrate the potency of this approach by deriving the upper limit to the speed of signal propagation in the XY spin chain.