ommunity's need for any quantum information theory (QIT)? While some genuine interest has been raised by the outcome of quantum cryptography, or more accurately, quantum key distribution (QKD), there is at present not enough matter of concern or driving market factor to bring QIT into the core of telecoms. The situation is made even more confused through the fact that information theory and quantum information theory appear to have little in common, or that the parallels between the two can be established only at the expense of advanced specialization. The telecom scientist is thus left with unsolved questions. For instance, what is quantum information, and how is it different from Shannon's theorem? How is information carried by qubits, as opposed to classical bits? How do IT theorems translate into QIT? What are the ultimate algorithms for quantum information compression, error correction, and encryption, and what benefit do they provide, compared with classical approaches? What are the main conceptual realizations of quantum information processing? The curious might peruse reference books, key papers, or Internet cross-references and tutorials, but xviii Introduction this endeavor leaves little chance of reaching satisfying conclusions, let alone acquiring solid grounds for pointing to future research directions. To summarize, on one hand, we find the old-and-forgotten IT field, with its wealth of very mature applications in all possible areas of information processing. On the other hand, we find the more recent and poorly known QIT field, showing high promise, but little potential of application within reasonable sight. In between, the difficulty for nonspecialists to make sense of any parallels between the two, and the lack of motivation to dig into what appears an austere or intractable bunch of mathematical formalism. The above description suggests the reason why this book was written, and its key purpose. Primarily, it is my belief that IT is incomplete without QIT, and that the second should not be appro