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

Understand

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.