Abstract
A definition of a quantum stochastic process (QSP) in discrete time capable of describing non-Markovian effects is introduced. The formalism is based directly on the physically relevant correlation functions. The notion of complete positivity is used as the main mathematical tool. Two different but equivalent canonical representations of a QSP in terms of completely positive maps are derived. A quantum generalization of the Kolmogorov-Sinai entropy is proved to exist.
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