We study multipartite super dense coding in the presence of a covariant noisy channel. We investigate the case of many senders and one receiver, considering both unitary and non-unitary encoding. We study the scenarios where the senders apply local encoding or global encoding. We show that, up to some pre-processing 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 super dense coding capacity is explicitly determined.
@article{arxiv.1203.1197,
title = {Distributed super dense coding over noisy channels},
author = {Zahra Shadman and Hermann Kampermann and Chiara Macchiavello and Dagmar Bruss},
journal= {arXiv preprint arXiv:1203.1197},
year = {2012}
}