Unital Positive Maps and Quantum States
  We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory. 
M. Asorey, A. Kossakowski, G. Marmo and E.C.G. Sudarshan