Polar codes in quantum information theory

Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results for polar coding in quantum information theory, including applications to classical-quantum multiple access channels, interference channels and compound communication settings, including the first proof of channel coding achieving the Han-Kobayashi rate region of the interference channel without the need of a simultaneous decoder. Moreover we add to the existing framework by extending polar codes to achieve the asymmetric capacity and improving the block error probability for classical-quantum channels. In addition we use polar codes to prove a new achievable rate region for the classical-quantum broadcast channel. We also discuss polar codes for quantum communication over quantum channels and state results towards codes for compound quantum channels in this setting. We conclude by stating a list of interesting open questions to invite further research on the topic.