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

2008/03/21 by Kimikazu Kato, Kato, Kimikazu
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #FOS: Physical sciences #Polynomial and algebraic computation #Quantum Physics (quant-ph) #Topological and Geometric Data Analysis #quant-ph

paper · pdf · doi:10.48550/arxiv.0803.3109

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

openalex publication_date 2008/03/21 · arxiv created 2008/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Quantum Algorithms Revisited
• Quantum theory, the Church–Turing principle and the universal quantum computer
• Simulating physics with computers
• Quantifying Entanglement

Related

• Voronoi Diagrams and a Numerical Estimation of a Quantum Channel Capacity
• Voronoi Diagrams for Pure 1-qubit Quantum States
• On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation
• Numerical ranges and geometry in quantum information: Entanglement, uncertainty relations, phase transitions, and state interconversion
• Quantum Entanglement and Geometry