Any-to-any quantum direct communication with superdense coding and decoy states

An efficient any-to-any quantum secure direct communication network scheme is proposed with quantum superdense coding and decoy states. The servers on the network prepare and measure the quantum signal, i.e., a sequence of the $d$-dimension Bell states. After confirming the security of the photons received from the receiver, the sender codes his secret message on them directly. For preventing a dishonest server from eavesdropping, some decoy photons prepared by measuring one photon in the Bell states are used to replace some original photons. One of the users on the network can communicate any other one. This scheme has the advantage of high capacity, and it is more convenient than others as only a sequence of photons is transmitted in quantum line