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

Classicality from Quantum Stochastic Processes