On generating quantum processes

The talk is devoted to the quantum processes consisting of generating and generated quantum channels. Such channels have been introduced earlier in the paper by R.N. Gumerov and R.L. Khazhin (Proc. Steklov Inst. Math. 324 (2024) (to appear)). For quantum processes, we discuss the property to be completely positive divisible. As an example, a phase-damping process is considered. We obtain a criterion for this quantum process to be completely positive divisible.