  Partial transport barriers in the chaotic sea of Hamiltonian systems
influence classical transport, as they allow for a small flux between chaotic
phase-space regions only. We establish for higher-dimensional systems that
quantum transport through such a partial barrier follows a universal transition
from quantum suppression to mimicking classical transport. The scaling
parameter involves the flux, the size of a Planck cell, and the localization
length due to dynamical localization along a resonance channel. This is
numerically demonstrated for coupled kicked rotors with a partial barrier that
generalizes a cantorus to higher dimensions.
