On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation

Details On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation

2006-07-04

arxiv.org/abs/quant-ph/0607029v1

Physics

Quantum Physics

6 pages, 2 figures, presented at the International Symposium on Voronoi Diagrams 2006 (ISVD2006)

Scientific paper

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.

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