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In this paper we shall consider the stratified manifold of quantum states andthe vector fields which act on it. In particular, we show that theinfinitesimal generator of the GKLS evolution is composed of a generator ofunitary transformations plus a gradient vector field along with a Kraus vectorfield transversal to the strata defined by the involutive distributiongenerated by the former ones.

Dynamical Vector Fields on the Manifold of Quantum States