  We give a new geometric interpretation of quantum pure states. Using
  Voronoi diagrams, we reinterpret the structure of the space of pure states as
a subspace of the quantum state space. In addition to the known coincidence of
some Voronoi diagrams for one-qubit pure states, we will show that even for
mixed one-qubit states, as far as sites are given as pure states, the Voronoi
diagram with respect to some distances -- the divergence, the Bures distance,
and the Euclidean distance -- are all the same.
  As to higher level pure quantum states, for the divergence, the
  Fubini-Study distance, and the Bures distance, the coincidence of the
diagrams still holds, while the coincidence of the diagrams with respect to the
divergence and the Euclidean distance no longer holds. That fact has a
significant meaning when we try to apply the method used for a numerical
estimation of a one-qubit quantum channel capacity to a higher level system.
