Distributed quantum dense coding enhanced with nonclassical routing

We propose a distributed quantum dense coding protocol that uses a control system to superpose two dense coding processes, allowing us to simultaneously and coherently encode and non-classically route the sender's single-qubit system to two receiver labs. We find that dense coding with coherently controlled encoding and routing performs better than the standard dense coding protocol in both global and one-way local decoding strategies employed by receiver labs in weak entanglement regimes and with noisy mixed states. We extend the protocol to incorporate noisy channels and show that, there exists a certain noise strength below which our protocol outperforms the noiseless standard dense coding protocol in presence of quantum dephasing noise. We extend our protocol to an arbitrary number of receivers and analyse its performance under a global decoding strategy.