Imprinting a complete information about a quantum channel on its output   state
  We introduce a novel property of bipartite quantum states, which we call "faithfulness", and we say that a state is faithful when acting with a channel on one of the two quantum systems, the output state carries a complete information about the channel. The concept of faithfulness can also be extended to sets of states, when the output states patched together carry a complete imprinting of the channel. 
Giacomo Mauro D'Ariano and Paoloplacido Lo Presti