  The quantum speed limit time of open system models is explored using the
Wasserstein-1-distance and the Wigner function. Use is made of the phase
covariant and a two-qubit model interacting with a squeezed thermal bath via
position-dependent coupling. The dependence of the coupling on the position of
the qubits allowed the study of the dynamics in the collective regime, which is
conducive to speeding up the evolution. The use of the Wigner function
naturally allows the study of the quantumness of the systems studied. An
interesting interplay is observed between non-Markovian behavior, quantumness,
and the quantum speed limit time. The presence of quantum correlations is seen
to speed up the evolution.
