Classical codes for quantum broadcast channels

TL;DR

This paper extends classical broadcast channel coding schemes to quantum channels, introducing quantum superposition and Marton coding techniques, and proving achievable rate regions using quantum simultaneous decoding methods.

Contribution

It provides the first quantum generalizations of superposition and Marton coding schemes for broadcast channels, with rigorous proofs of their achievable rate regions.

Findings

Quantum superposition coding achieves a known classical rate region.

Quantum Marton coding extends classical bounds to quantum broadcast channels.

Utilizes recent quantum simultaneous decoding techniques for error analysis.

Abstract

We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a proof of the rate region stated in [Yard et al., IEEE Trans. Inf. Theory 57 (10), 2011]. Our second result is a quantum generalization of the Marton coding scheme. The error analysis for the quantum Marton region makes use of ideas in our earlier work and an idea recently presented by Radhakrishnan et al. in arXiv:1410.3248. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.