Convergence Analysis for Discrete-Time Quantum Semigroup

In this work the asymptotic behavior of completely-positive trace-precerving maps is analyzed. First, the probabilities of converging to invariant subspaces, in the limit of infinite iteration, are studied. Next, two different decompositions of the quantum system's Hilbert space are introduced, both aimed to analyze the convergence behavior and speed. Finally the possibilities that the dynamics converges to a subspace, after a finite amount of time, is investigated