Quantum Information Theory in Infinite Dimensions with Application to Optical Channels

Abstract

AbstractInformation theory deals with the efficient representation of information sources as well as providing fundamental limits to the amount of information communicated reliably over channels. These sources and channels are generally classical, i.e., represented by standard probability distributions. Quantum information theory takes it to the next level where we allow for the sources as well as channels to be quantum. From the representation of quantum states to the communication over quantum channels, the theory not only essentially encapsulates classical information theoretic methods but also accounts for quantum effects such as superposition, entanglement, interference, etc. In this article, we will review and focus on the information theoretic analysis of quantum channels with infinite dimensions. Infinite dimensionality is needed to model quantum optical channels which are ubiquitous in today’s practical networks, distributed quantum communication and quantum internet. The infinite dimensionality introduces some unique problems when compared with finite-dimensional channels and has not been deeply explored in literature from the quantum information theoretic perspective. For these channels, we provide the essential concepts and state-of-the-art channel capacity results. To make this paper self-contained, we also recall the finite dimensional results.