How Well a Chaotic Quantum System Can Retain Memory of Its Initial State?

In classical mechanics the local exponential instability effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. We relate the latter fact to the low (at most linear) rate with which the system's Wigner function gets during evolution more and more complicated structure and establish existence of a critical strength of external influence below which such a memory still survives.