  We consider a bipartite quantum system S=AB such that the part A is isolated
from the environment E and only the part B interacts with E. Under such
circumstances, entanglement of the system may experience decreases and
increases, during the evolution of the system. Here, we show that the
entanglement of the system can exceed its initial value, under such local
interaction, even though, at the initial moment, there is no entanglement in
the environment and the system and the environment are only classically
correlated. The case which is studied in this paper possesses another
interesting feature too: The reduced dynamics of the system can be modeled as a
completely positive map. In addition, we introduce the concept of inaccessible
entanglement to explain why entanglement can exceed its initial value, under
local interactions, in open quantum systems.
