  We consider the problem of characterizing an inner bound to the capacity
region of a $3-$user classical-quantum interference channel ($3-$CQIC). The
best known coding scheme for communicating over CQICs is based on unstructured
random codes and employs the techniques of message splitting and superposition
coding. For classical $3-$user interference channels (ICs), it has been proven
that coding techniques based on coset codes - codes possessing algebraic
closure properties - strictly outperform all coding techniques based on
unstructured codes. In this work, we develop analogous techniques based on
coset codes for $3$to$1-$CQICs - a subclass of $3-$user CQICs. We analyze its
performance and derive a new inner bound to the capacity region of
$3$to$1-$CQICs that subsume the current known largest and strictly enlarges the
same for identified examples.
