  Quantum steering means that in some bipartite quantum systems, the local
measurements on one side can determine the state of the other side. Here we
show that in high-dimensional systems, there exists a specific entangled state
which can display a kind of chaos effect when being adopted for steering. That
is, a subtle difference in the measurement results on one side can steer the
other side into completely orthogonal states. Moreover, by expanding the result
to infinite-dimensional systems, we find two sets of states for which, contrary
to common belief, even though their density matrices approach being identical,
the steering between them is impossible. This property makes them very useful
for quantum cryptography.
