The transition from quantum to classical, in the case of a quantum harmonic
oscillator, is typically identified with the transition from a quantum
superposition of macroscopically distinguishable states, such as the
Schr\"odinger cat state, into the corresponding statistical mixture. This
transition is commonly characterized by the asymptotic loss of the interference
term in the Wigner representation of the cat state. In this paper we show that
the quantum to classical transition has different dynamical features depending
on the measure for nonclassicality used. Measures based on an operatorial
definition have well defined physical meaning and allow a deeper understanding
of the quantum to classical transition. Our analysis shows that, for most
nonclassicality measures, the Schr\"odinger cat dies after a finite time.
Moreover, our results challenge the prevailing idea that more macroscopic
states are more susceptible to decoherence in the sense that the transition
from quantum to classical occurs faster. Since nonclassicality is prerequisite
for entanglement generation our results also bridge the gap between
decoherence, which appears to be only asymptotic, and entanglement, which may
show a sudden death. In fact, whereas the loss of coherences still remains
asymptotic, we have shown that the transition from quantum to classical can
indeed occur at a finite time.Comment: 9+epsilon pages, 4 figures, published version. Originally submitted
as "Sudden death of the Schroedinger cat", a bit too cool for APS policy :-