For the case of phase damping (pure decoherence) we investigate the extent to which environmental traits are imprinted on an open quantum system. The dynamics is described using the quantum channel approach. We study what the knowledge of the channel may reveal about the nature of its underlying dynamics and, conversely, what the dynamics tells us about how to consistently model the environment. We find that for a Markov phase-damping channel, that is, a channel compatible with a

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... Markovian evolution, the environment may adequately be represented by a mixture of only a few coherent states. For arbitrary Hilbert space dimension N≥ 4 we refine the idea of quantum phase damping, of which we show a means of identification. Symmetry considerations are used to identify decoherence-free subspaces of the system.