  Chaotic eigenstates of quantum systems are known to localize on either side
of a classical partial transport barrier if the flux connecting the two sides
is quantum mechanically not resolved due to Heisenberg's uncertainty.
Surprisingly, in open systems with escape chaotic resonance states can localize
even if the flux is quantum mechanically resolved. We explain this using the
concept of conditionally invariant measures from classical dynamical systems by
introducing a new quantum mechanically relevant class of such fractal measures.
We numerically find quantum-to-classical correspondence for localization
transitions depending on the openness of the system and on the decay rate of
resonance states.
