Variational learning the SDC quantum protocol with gradient-based optimization

Recently, a variational learning approach is adopted to discover quantum communication protocols (Wan et al. in npj Quantum Inf 3:36, 2017). Because designing quantum protocols manually is a delicate and difficult work, this variational learning approach is well worth further study. In this paper, we use the same approach to learn the simultaneous dense coding (SDC) protocols with two or three receivers. The gradient-based optimization is used to learn the parameters of the locking operator of the SDC protocol. Two different designs of the loss function are considered. Numerical experiment results show the effectiveness of this variational learning approach.