Quantum channels and their entropic characteristics

TL;DR

This paper surveys the properties and entropic measures of quantum channels, emphasizing their role in quantum information processing, including finite and continuous-variable systems, and highlighting entanglement as a key resource.

Contribution

It provides a comprehensive overview of quantum channels and their entropic characteristics, integrating examples and discussing the significance of entanglement in quantum communication.

Findings

Quantum channels are fundamental in quantum information theory.

Entropic quantities like channel capacities characterize information processing.

Entanglement serves as a crucial resource in quantum communication.

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.