Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics

TL;DR

This paper extends the Lieb-Robinson bound to general Markovian quantum dynamics, showing a maximum signal propagation speed and correlation decay in stationary states, thus broadening its applicability in quantum physics.

Contribution

It generalizes the Lieb-Robinson bound to Markovian quantum evolution and demonstrates correlation decay in stationary states based on this bound.

Findings

Lieb-Robinson bound holds for Markovian quantum dynamics.

Correlations decay exponentially in stationary states.

Signal propagation speed is bounded by a generalized Lieb-Robinson velocity.

Abstract

The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general Markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length-scale set by the Lieb-Robinson velocity and the system's relaxation time.