Classical state sensitivity from quantum mechanics

Sensitivity of the time evolution to small changes in the state is a characteristic feature of classical chaos. It has been believed that state sensitivity could not exist in quantum mechanics because of the unitary invariance of the Hilbert-space overlap of states. We argue that this Hilbert-space criterion is irrelevant and show that both quantum states and classical statistical states exhibit a similar kind of state sensitivity. This is demonstrated by the degree to which the initial state can be recovered in computational motion reversal: forward evolution for a time T, perturbation of the state, and backward time evolution. Some differences between classical and quantum state sensitivity remain, and these seem to be insensitive to decoherence. {} 1996 The American Physical Society.