We show some coincidences of Voronoi diagrams in a quantum state space with respect to some distances. This means a computational geometry interpretation of a structure of a quantum state space. More properly, we investigate the Voronoi diagrams with respect to the divergence, Fubini-Study distance, Bures distance, geodesic distance and Euclidean distance. As an application of it, we explain an effective algorithm tocompute the Holevo capacity of one-qubit quantum channel. The effectiveness of the algorithm is supported by the coincidence of Voronoi diagrams. Moreover, our result provides insights into the applicability of the same method to a higher level system. © 2009 Springer-Verlag Berlin Heidelberg.