Extreme Points and Factorizability for New Classes of Unital Quantum Channels

We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family channels given by completely positive (CP) maps $M_3({\bf C}) \mapsto M_3({\bf C})$ which are both trace-preserving. Almost every member this is factorizable extreme in the set CP trace-preserving, but not either or trace-preserving maps. also large generalize Werner-Holevo channel for $d = 3$ sense that they defined terms partial isometries rank $d-1$. Moreover, we extend to whose Kraus operators have form $t |e_j \rangle \langle e_j | \oplus V $ with $V \in M_{d-1} ({\bf unitary (-1,1)$. show almost map analyze detail particularly interesting subclass unless -1/(d-1)$. For 3$, includes pair dual factorization can be obtained taking trace over different subspaces after using same conjugation \otimes C})$.