Quantum information processing is an exciting new emergent and interdisciplinary field. It combines questions of national security (When will today's public key cryptography be broken?) to questions of fundamental science (What are the fundamental limits to information processing?). It has thrived through the collaboration between the computer, engineering, mathematical and physical sciences. It is a field that is challenging our understanding of information, communication, computation, and of the fundamental laws of nature. This book brings together leading research in the field.