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Quantum dynamics of the density operator in the framework of a singleprobability vector is analyzed. In this framework quantum states define aproper convex quantum subset in an appropriate simplex. It is showed that thecorresponding dynamical map preserving a quantum subset needs not be stochasticcontrary to the classical evolution which preserves the entire simplex.Therefore, violation of stochasticity witnesses quantumness of evolution.

Stochastic evolution of finite level systems: classical vs. quantum