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

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.

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

References in corpus (27)

• Mixed State Entanglement and Quantum Error Correction
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• Quantum Algorithms Revisited
• Quantum computers can search rapidly by using almost any transformation
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Additivity for a class of unital qubit channels
• Grover's Quantum Search Algorithm for an Arbitrary Initial Amplitude Distribution
• The Capacity of Quantum Channel with General Signal States
• Quantum Sub-Gaussian Mean Estimator
• Fast quantum algorithms for numerical integrals and stochastic processes
• Asymptotic estimation theory for a finite dimensional pure state model
• Geometric Strategy for the Optimal Quantum Search
• Entanglement purification via separable superoperators
• Entanglement Cost of Antisymmetric States and Additivity of Capacity of Some Quantum Channel
• A quantum protocol to win the graph colouring game on all Hadamard graphs
• Voronoi Diagrams for Pure 1-qubit Quantum States
• A quantum channel with additive minimum output entropy
• An application of a matrix inequality in quantum information theory
• Comments on multiplicativity of maximal p-norms when p = 2
• Note on multiple additivity of minimal Renyi entropy output of the Werner-Holevo channels
• Voronoi Diagrams and a Numerical Estimation of a Quantum Channel Capacity
• On a Geometric Structure of Pure Multi-qubit Quantum States and Its Applicability to a Numerical Computation
• Additivity for transpose depolarizing channels
• From Monte Carlo to Quantum Computation
• Remark on the additivity conjecture for the quantum depolarizing channel