Computing and controlling the convergence speed of a quantum dynamical semigroup

The speed of convergence of controlled dissipative dynamics to the desired state or set of states is critical in many tasks in experimental physics and quantum information processing. Here we focus on quantum Markovian master equations and, by exploiting the linear character of the dynamical generator, we derive an alternative characterization of the semigroups stabilizing a target subspace, as well as the asymptotic speed of convergence to the desired set. Our analysis highlights the effect of the Hamiltonian parameters (which can be considered as our controls) on the convergence speed, and suggests two basic principles for their design.