Mathematical Models of Markovian Dephasing

We develop a notion of dephasing under the action of a quantum? Markov semigroup in terms of convergence of operators to a block-diagonal? form determined by irreducible invariant subspaces. If the latter are all ?one-dimensional, we say the dephasing is maximal. We study characterization ?of a maximally dephasing evolution in terms of unitary dilations ?with only classical noise. In particular, we introduce an intrinsic? quantity constructed from the generator which quantities the? degree of obstruction to having a classical diffusive noise model.? (Joint work with J.E. Gough, H.I. Nurdin and L. Viola)?