  For 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.
