Holevo A.S. Quantum Systems, Channels, Information: A Mathematical Introduction

Walter de Gruyter, 2012. — 361 p. — ISBN: 9783110273250.Quantum information theory studies the general laws of transfer, storage and processing information in systems obeying the laws of quantum mechanics. It took shape as a self-consistent area of research in the 1990s, while its origin can be traced back to the 1950-1960s, which was when the basic ideas of reliable data transmission and of Shannon's information theory were developed. At the first stage, which covers the period 1960-1980, the main issue consisted of the fundamental restrictions on the possibilities of information transfer and processing caused by the quantum-mechanical nature of its carrier. Modern technological developments, relying upon the achievements of quantum electronics and quantum optics, suggest that in the foreseeable future such restrictions will become the main obstacle limiting further extrapolation of existing technologies and principles of information processing.
The emergence, in the 1980-1990s, of the ideas of the quantum computing, quantum cryptography and the new communication protocols, on the other hand, allowed discussing not only the restrictions, but also the new possibilities created by the use of specific quantum resources, such as quantum entanglement, quantum complementarity, and quantum parallelism. Quantum information theory provides the clue to understanding these fundamental issues, and stimulates the development of experimental physics, with potential importance to new, effective applications. At present, investigations in the area of quantum information science, including information theory, its experimental aspects and technological developments, are ongoing in advanced research centers throughout the world.Basic structures
Vectors and operators
States, observables, statistics
Composite systems and entanglement
The primary coding theorems
Classical entropy and information
The classical-quantum channel
Channels and entropies
Quantum evolutions and channels
Quantum entropy and information quantities
The classical capacity of quantum channel
Entanglement-assisted classical communication
Transmission of quantum information
Channels with constrained inputs
Gaussian systems