> Throwing away this information and taking an ensemble average, you'd see an exponential decay of coherence. That is described by a density matrix but is not

> Throwing away this information and taking an ensemble average, you'd see an exponential decay of coherence. That is described by a density matrix but is not a pure state. The true state may be a pure state (because as you said the systems are separable after the measurement) but our description is a mixture reflecting our imperfect information (and not a superposition of the pure states corresponding to the potential outcomes).