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We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord. [ABSTRACT FROM AUTHOR]

We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via the spectral analysis of the corresponding time-dependent generators. We consider both Markovian and non-Markovian cases. [ABSTRACT FROM AUTHOR]

We analyze special class of bipartite states - so-called Bell diagonal states. In particular, we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis. [ABSTRACT FROM AUTHOR]

Complete characterization of complete positivity preserving non-Markovian master equations is presented. [ABSTRACT FROM AUTHOR]