  We consider a multi-level system coupled to a bosonic measurement apparatus.
We derive exact expressions for the time-dependent expectation values of a
large class of physically relevant observables that depend on degrees of
freedom of both sytems. We find that, for this class, though the two systems
become entangled as a result of their interaction, they appear classically
correlated for long enough times. The unique corresponding separable state is
determined explicitly. To better understand the physical parameters that
control the time scale of this effective disentanglement process, we study a
one-dimensional measurement apparatus.
