Finite-time quantum-to-classical transition for a Schroedinger-cat state

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 Schroedinger-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 state 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 a prerequisite for entanglement generation
our results also bridge the gap between decoherence, which is lost
only asymptotically, and entanglement, which may show a sudden death.
In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at
a finite time.