Quantum Information Theory: Classical Communication Over Quantum Channels

This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity