Quantum channels and their entropic characteristics

Abstract

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the "continuous-variables" case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations - entanglement - as a novel communication resource, is stressed.

review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys. (in press)

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• Quantum states tomography with noisy measurement channels
• Quantum probabilities and entanglement for multimode quantum systems
• Non-Markovianity as a Resource for Quantum Technologies
• Deterministic preparation of superpositions of vacuum plus one photon by adaptive homodyne detection: experimental considerations
• Process Tomography for Systems in a Thermal State
• Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic
• Quantum theory of measurements as quantum decision theory
• Positive operator-valued measures in quantum decision theory
• Decoding Protocols for Classical Communication on Quantum Channels
• On the additivity of the minimum output entropy