Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics

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.

References in corpus (3)

• Propagation of Correlations in Quantum Lattice Systems
• Lieb-Robinson bounds for commutator-bounded operators
• Quantum Adiabatic Computation With a Constant Gap is Not Useful in One Dimension

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