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We consider a multi-level system coupled to a bosonic measurement apparatus.We derive exact expressions for the time-dependent expectation values of alarge class of physically relevant observables that depend on degrees offreedom of both sytems. We find that, for this class, though the two systemsbecome entangled as a result of their interaction, they appear classicallycorrelated for long enough times. The unique corresponding separable state isdetermined explicitly. To better understand the physical parameters thatcontrol the time scale of this effective disentanglement process, we study aone-dimensional measurement apparatus.

Effective disentanglement of measured system and measurement apparatus