A simple proof of the Jamiolkowski criterion for complete positivity of   linear maps
  We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a systematic method to give any set of Kraus matrices of its Kraus decomposition. 
D. Salgado, J.L. Sanchez-Gomez and M. Ferrero