Generalizations of Pauli channels
  The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main examples appear on bipartite systems 
Denes Petz and Hiromichi Ohno