  Time-reversibility measured by the deviation of the perturbed time-reversed
motion from the unperturbed one is examined for normal quantum diffusion
exhibited by four classes of quantum maps with contrastive physical nature.
Irrespective of the systems, there exist a universal minimal quantum threshold
above which the system completely loses the past memory, and the time-reversed
dynamics as well as the time-reversal characteristics asymptotically trace
universal curves independent of the details of the systems.
