  Quantum operations are usually defined as completely positive (CP), trace
preserving (TP) maps on quantum states, and can be represented by operator-sum
or Kraus representations. In this paper, we calculate operator-sum
representation and master equation of an exactly solvable dynamic of one-qubit
open system in layered environment . On the other hand, we obtain exact
Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the
maps. Finally, we study a simple example to consider the relation between CP
maps and initial quantum correlation and show that vanishing initial quantum
correlation is not necessary for CP maps.
