Abstract
The reduced dynamics of an open quantum system S, interacting with its environment E, is not completely positive, in general. In this paper, we demonstrate that if the two following conditions are satisfied, simultaneously, then the reduced dynamics is completely positive: (1) the reduced dynamics of the system is linear, for arbitrary system-environment unitary evolution U; and (2) the reduced dynamics of the system is linear, for arbitrary initial state of the system ρ_S.