2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115814For one-qubit pure quantum states, it is already proved that the Voronoi diagrams with respect to two distances -- Euclidean distance and the quantum divergence -- coincide. This fact is a support for a known method to calculate the Holevo capacity. To consider an applicability of this method to quantum states of a higher level system, it is essential to check if the coincidence of the Voronoi diagrams also occurs. In this paper, we show a negative result for that expectation. In other words, we mathematically prove that those diagrams no longer coincide in a higher dimension. That indicates that the method used in one-qubit case to calculate the Holevo capacity might not be effective in a higher dimension.6 pages, 2 figures, presented at the International Symposium on Voronoi Diagrams 2006 (ISVD2006)Quantum Physicstext