Three-step three-party quantum secure direct communication

We propose a three-party quantum secure direct communication (QSDC) protocol with hyperentanglement in both spatial-mode and polarization degrees of freedom. The secret message can be encoded independently with desired unitary operations in two degrees of freedom. In this protocol, a party can synchronously obtain the other two parties' messages. Compared with previous three-party QSDC protocols, our protocol has several advantages. First, the single photons in our protocol are only required to transmit for three times. This advantage makes this protocol simple and useful. Second, Alice and Bob can send different secret messages to Charlie, respectively. Finally, with hyperentanglement, this protocol has a higher information capacity than other protocols.