Achievable Rate Regions for Multi-terminal Quantum Channels via Coset Codes

We undertake a Shannon theoretic study of the problem of communicating classical information over (i) a $3-$user quantum interference channel (QIC) and (ii) a $3-$user quantum broadcast channel (QBC). Our focus is on characterizing inner bounds. In our previous work, we had demonstrated that coding strategies based on coset codes can yield strictly larger inner bounds. Adopting the powerful technique of \textit{tilting}, \textit{smoothing} and \textit{augmentation} discovered by Sen recently, and combining with our coset code strategy we derive a new inner bound to the classical-quantum capacity region of both the $3-$user QIC and $3-$user QBC. The derived inner bound subsumes all current known bounds.