Superdense Coding Through Repeaterless Hybrid Network of Depolarizing Quantum Communication Channels

Superdense coding is a fundamental protocol in quantum communication, which enables us to send two bits of information by the transmission of just a single qubit. In this paper, we consider superdense coding through a noisy quantum depolarizing channel. Following a simple calculation, we derive superdense coding capacity as a function of depolarizing probability. We extend this derivation to the scenario of repeaterless series-cascaded depolarizing channels and provide an elementary approach to evaluate the maximal intervals in which repeaters shall need to be placed in such a cascaded system. Finally, we validate the theoretical results via a Monte Carlo simulation, simultaneously providing a generalized framework. We believe that our numerical results serve as a useful benchmark and give a base to extend such simulations to other quantum channels.