Bidirectional Quantum Secure Direct Communication Network Protocol with Hyperentanglement

We propose a bidirectional quantum secure direct communication (QSDC) network protocol with the hyperentanglment in both the spatial-mode ad the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. Compared with other QSDC network protocols, our QSDC network protocol has a higher capacity as each photon pair can carry 4 bits of information. Also, we discuss the security of our QSDC network protocol and its feasibility with current techniques.