Abstract

The notions of channel and capacity are central to the classical Shannon theory. “Quantum Shannon theory” denotes a subfield of quantum information science which uses operator analysis, convexity and matrix inequalities, asymptotic techniques such as large deviations and measure concentration to study mathematical models of communication channels and their information-processing performance. From the mathematical point of view quantum channels are normalized completely positive maps of operator algebras, the analog of Markov maps in the noncommutative probability theory, while the capacities are related to certain norm-like quantities. In applications noisy quantum channels arise from irreversible evolutions of open quantum systems interacting with environment-a physical counterpart of a mathematical dilation theorem.