  By using the pseudo-metric introduced in [F. Golse, T. Paul: Archive for
Rational Mech. Anal. 223 (2017) 57-94], which is an analogue of the Wasserstein
distance of exponent $2$ between a quantum density operator and a classical
(phase-space) density, we prove that the convergence of time splitting
algorithms for the von Neumann equation of quantum dynamics is uniform in the
Planck constant $\hbar$. We obtain explicit uniform in $\hbar$ error estimates
for the first order Lie-Trotter, and the second order Strang splitting methods.
