1 research outputs found
Voronoi Diagrams for Quantum States and Its Application to a Numerical Estimation of a Quantum Channel Capacity
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.Comment: Ph.D thesis, adviser: Hiroshi Imai, 118 pages, 15 figures, 2 table