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We introduce a concept of Kadison-Schwarz divisible dynamical maps. It turnsout that it is a natural generalization of the well known CP-divisibility whichcharacterizes quantum Markovian evolution. It is proved that Kadison-Schwarzdivisible maps are fully characterized in terms of time-local dissipativegenerators. Simple qubit evolution illustrates the concept.

Dissipative generators, divisible dynamical maps and Kadison-Schwarz inequality