  The well-known two-slit interference is understood as a special relation
between observable (localization at the slits) and state (being on both slits).
Relation between an observable and a quantum state is investigated in the
general case. It is assumed that the amount of ceherence equals that of
incompatibility between observable and state. On ground of this, an argument is
peresented that leads to a natural quantum measure of coherence, called
"coherence or incompatibility information". Its properties are studied in
detail making use of 'the mixing property of relative entropy' derived in this
article. A precise relation between the measure of coherence of an observable
and that of its coarsening is obtained and discussed from the intutitive point
of view. Convexity of the measure is proved, and thus the fact that it is an
information entity is established. A few more detailed properties of coherence
information are derived with a view to investigate final-state entanglement in
general repeatable measurement, and, more importantly, general bipartite
entanglement in follow ups of this study.
