On characterizations of bistochastic Kadison-Schwarz operators on   $M_2(\mathbb{C})$
  In this paper we describe bistochastic Kadison-Schawrz operators acting on $M_2(\mathbb{C})$. Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of that characterization we construct Kadison-Schawrz operators, which are not completely positive. 
Farrukh Mukhamedov, Hasan Akin
math.FA math-ph math.MP quant-ph