On light cone bounds in quantum open systems

Abstract: We study propagation of quantum information in few-body Markov quantum open systems (MQOS). For a large class of such systems, we prove the existence of an effective light cone with an exponentially small spill-over. We also prove a Lieb-Robinson-type bound and a lower bound on the delivery time of quantum messages. \par Mathematically, we describe space-time behavior of solutions of the von Neumann-Lindblad equation underlying the dynamics of MQOS, which is a natural extension of the Schr\"odinger equation and is a key example of a non-Abelian PDE of quantum physics.