Distributed superdense coding over noisy channels

We study multipartite superdense coding in the presence of a covariant noisy channel. We investigate the case
of many senders and one receiver, considering both unitary and nonunitary encoding. We study the scenarios
where the senders apply local encoding or global encoding. We show that, up to some preprocessing on the
original state, the senders cannot do better encoding than local, unitary encoding. We then introduce general
Pauli channels as a significant example of covariant maps. Considering Pauli channels, we provide examples for
which the superdense coding capacity is explicitly determined.