  The sum of the Holevo quantity (that bounds the capacity of quantum channels
to transmit classical information about an observable) and the quantum discord
(a measure of the quantumness of correlations of that observable) yields an
observable-independent total given by the quantum mutual information. This
split naturally delineates information about quantum systems accessible to
observers -- information that is redundantly transmitted by the environment --
while showing that it is maximized for the quasi-classical pointer observable.
Other observables are accessible only via correlations with the pointer
observable. Further, we prove an anti-symmetry property relating accessible
information and discord. It shows that information becomes objective --
accessible to many observers -- only as quantum information is relegated to
correlations with the global environment, and, therefore, locally inaccessible.
The resulting complementarity explains why, in a quantum Universe, we perceive
objective classical reality while flagrantly quantum superpositions are out of
reach.
