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Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics

David Poulin
Phys. Rev. Lett. 104, 190401 – Published 11 May 2010

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.

  • Figure
  • Received 31 March 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.190401

©2010 American Physical Society

Authors & Affiliations

David Poulin*

  • Département de Physique, Université de Sherbrooke, Québec, Canada

  • *David.Poulin@USherbrooke.ca

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Issue

Vol. 104, Iss. 19 — 14 May 2010

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