  The relation between the degree of entanglement and time scale of
time-irreversible behavior is investigated for classically chaotic quantum
coupled kicked rotors by comparing the entanglement entropy (EE) and the
lifetime of correspondence with classical decay of correlation, which was
recently introduced. Both increase {\it on average} drastically with a strong
correlation when the strength of coupling between the kicked rotors exceeds a
certain threshold. The EE shows an anomalously large fluctuation resembling a
critical fluctuation around the threshold value of coupling strength where the
entanglement sharply increases toward full entanglement. In this regime it can
be shown that, although the correlation is hidden, EE and the lifetime of {\it
individual eigenfunctions} also have a positive correlation that can be seen
via an another measure.
