Stuttgart 2012 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 31: Quanteninformation: Konzepte und Methoden 4
Q 31.6: Talk
Tuesday, March 13, 2012, 15:15–15:30, V7.01
Asymptotic Evolution of Quantum Markov Chains — •Jaroslav Novotny1 and Gernot Alber2 — 1FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto, Czech Republic — 2Institut für Angewandte Physik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can desribe different quantum protocols in the presence of decoherence.
A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.