One pure quasi quantum quadratic operators

In the literature on quantum information and communication systems, such a map is called a channel. Note that the concept of state in a physical system is a powerful weapon to study the dynamical behavior of that system. One of the important class of channels is so-called pure ones, which map pure states to pure ones. Therefore, it would be interesting characterize such kind of maps (or channels). In the present work we are going to describe pure quasi quantum quadratic operators.