Distributed super dense coding over noisy channels

TL;DR

This paper explores multipartite super dense coding over noisy channels, demonstrating that local unitary encoding is optimal and providing explicit capacity calculations for Pauli channels.

Contribution

It shows that, with pre-processing, local unitary encoding suffices and explicitly determines super dense coding capacities for Pauli channels in noisy environments.

Findings

Local unitary encoding is optimal with pre-processing.

Super dense coding capacity can be explicitly calculated for Pauli channels.

Global encoding does not outperform local encoding under the studied conditions.

Abstract

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.