Operator-sum representation of time-dependent density operators and its   applications
  We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples. 
D. M. Tong, L. C. Kwek, C. H. Oh, Jing-Ling Chen and L. Ma