Lower Bounds on the Capacities of Quantum Relay Channels

Three kinds of quantum relay communication models are proposed, i.e., the quantum single relay model, quantum serial multi-relay model and quantum parallel multi-relay model. The channel capacities of those three kinds of systems are analyzed with the theory of quantum Markov trace-preserving process and the generalized theory of simple multi-hop channel in quantum system. Motivated by the quantum Fano inequality, the lower bounds of that channel capacities are derived. The illustration and simulation present the trends of the lower bounds on the channel capacities of different quantum relay systems based on the depolarizing noisy channel.