  We give a proof of the multi-party typicality conjecture for the first
nontrivial case when there are only two parties. The conjecture itself is
motivated by the study of multi-party state merging protocols on quantum
systems. Our approach is based on fundamental group-theoretical properties,
thereby providing an opportunity to study the problem from a more systematic
perspective. Our proof also covers an extended multiparty typicality conjecture
that we state in this work. This extended multiparty typicality conjecture is
formulated using arbitrary $k$-norms instead of only the $2$-norm as in the
original conjecture.
