Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 81-85).In the first part, we present a family of entanglement purification protocols that generalize four previous methods, namely the recurrence method, the modified recurrence method, and the two methods proposed by Maneva-Smolin and Leung-Shor. We will show that this family of protocols have improved yields over a wide range of initial fidelities F, and hence imply new lower bounds on the quantum capacity assisted by two-way classical communication of the quantum depolarizing channel. In particular, we show that the yields of these protocols are higher than the yield of universal hashing for F less than 0.99999 and as F goes to 1. In the second part, we define, for any quantum discrete memoryless channel, quantum entanglement capacity with classical feedback, a quantity that lies between two other well-studied quantities. These two quantities - namely the quantum capacity assisted by two-way classical communication and the quantum capacity with classical feedback - are widely conjectured to be different. We then present adaptive protocols for this newly-defined quantity on the quantum depolarizing channel. These protocols in turn imply new lower bounds on the quantum capacity with classical feedback.by Alan W. Leung.Ph.D
