  1-qubit quantum states form a space called the three-dimensional Bloch ball.
To compute Holevo capacity, Voronoi diagrams in the Bloch ball with respect to
the quantum divergence have been used as a powerful tool. These diagrams
basically treat mixed quantum states corresponding to points in the interior of
the Bloch ball. Due to the existence of logarithm in the quantum divergence,
the diagrams are not defined on pure quantum states corresponding to points on
the two-dimensional sphere. This paper first defines the Voronoi diagrams for
pure quantum states on the Bloch sphere by the Fubini-Study distance and the
Bures distance. We also introduce other Voronoi diagrams on the sphere obtained
by taking a limit of Voronoi diagrams for mixed quantum states by the quantum
divergences in the Bloch ball. These diagrams are shown to be equivalent to the
ordinary Voronoi diagram on the sphere.
