Superiority in dense coding through non-Markovian stochasticity

We investigate the distributed dense coding (DC) protocol, involving multiple senders and a single or two receivers under the influence of non-Markovian noise, acting on the encoded qubits transmitted from the senders to the receiver(s). We compare the effects of non-Markovianity on DC for both the dephasing and depolarizing channels. In the case of dephasing channels, we illustrate that for some classes of states, high non-Markovian strength can eradicate the negative influence of noisy channels which is not observed for depolarizing noise. Furthermore, we incorporate randomness into the noise models by replacing the Pauli matrices with random unitaries and demonstrate the constructive impact of stochastic noise models on the quenched averaged dense coding capacity. Interestingly, we report that the detrimental effect of non-Markovian depolarizing channels in the DC protocol can be eliminated when randomness is added to the channel.