  I develop a theory of classicality from quantum systems. This theory stems
from the study of classical and quantum stationary stochastic processes. The
stochastic processes are characterized by polyhedral (classical) and
semidefinite representative (quantum) cones. Based on a previous result by the
author I expand the study of fixed points from quantum channels. I give a
semidefinite program that characterizes a quantum channel separating into a
core and a part that decays with many iterations. In general, the solution is
non-separable in the space it is defined. I present a characterization of
channels in terms of their fixed points for the separable case. A quantum
simulation of a polyhedral cone can then be constructed.
