Quantum Information Theory

Abstract

The present chapter introduces the mathematical modeling of quantum communication systems in the spirit of Shannon’s conception of information theory. Regarding the choice of topics treated as well as the methodological approach pursued, one can draw analogies with the material covered in standard classical information theory modules, which are intended for master’s as well as bachelor’s students of electrical engineering and communication sciences, among other majors. After covering the rather fundamental communication protocols, we move on to more advanced models in which communication involving different types of quantum channels can be performed. Topics covered in the chapter include, quantum teleportation and dense coding, quantum hypothesis testing, source coding for memoryless quantum sources and coding theorems for classical message transmission over quantum and classical quantum memoryless channels. We conclude the chapter with selected advanced topics such as information-theoretic security for quantum channels, optimal protocols for generation of classical and quantum resources and finally, communication under more realistic models such as the compound and arbitrarily varying channels.