Summary
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 to compute 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.
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Kato, K., Oto, M., Imai, H., Imai, K. (2009). Computational Geometry Analysis of Quantum State Space and Its Applications. In: Gavrilova, M.L. (eds) Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Studies in Computational Intelligence, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85126-4_4
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DOI: https://doi.org/10.1007/978-3-540-85126-4_4
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