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In the present paper we study quasi quantum quadratic operators (q.q.o) acting on the algebra of 2 × 2 matrices M2(C). We describe quasi q.q.o. with Haar state, and prove that if a symmetric quasi q.q.o. with Haar state is q-pure, then it cannot be positive.International Conference on Mathematical Sciences and Statistics 2013Adem Kilicman • Wah