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

TL;DR

This paper introduces a geometric approach using Voronoi diagrams and smallest enclosing balls to analyze quantum states and efficiently estimate quantum channel capacity.

Contribution

It presents a novel computational geometric interpretation of quantum state space and applies it to estimate quantum channel capacity.

Findings

Voronoi diagrams effectively model quantum state adjacency.

The method improves quantum channel capacity estimation.

Geometric tools facilitate analysis of quantum information structures.

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.