  We simulate a free dissipative and coherent-driven Kerr nonlinear system
using a time-evolving block decimation (TEBD) algorithm, to study the impact of
the initial state on the exact quantum dynamics of the system. The
superposition of two coherent branches results in non-classical time dynamics.
The Wigner state representation confirms that the system ends up saturating to
two different branches, through evolving different trajectories, resulting in
de-Gaussification throughout evolution. Furthermore, we also see that the time
evolution suffers a residual effect of the initial state.
