Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity

Details Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity

2008-03-21

arxiv.org/abs/0803.3109v2

Physics

Quantum Physics

Ph.D thesis, adviser: Hiroshi Imai, 118 pages, 15 figures, 2 tables

Scientific paper

In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum system. Especially we introduce the concept of the Voronoi diagram and the smallest enclosing ball problem to the space of quantum states. With those tools in computational geometry, we analyze the adjacency structure of a point set in the quantum state space. Additionally, as an application, we show an effective method to compute the capacity of a quantum channel.

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