Information Leakage in Efficient Bidirectional Quantum Secure Direct Communication with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom

Recently, Wang et al. presented a bidirectional quantum secure direct communication protocol with single photons in both polarization and spatial-mode degrees of freedom (Int. J. Theor. Phys. 54(10): 3443-3453, 2015). They claimed that their protocol was efficient and removed the drawback of information leakage. However, we found that the information leakage actually exists in their protocol. In this paper, we analyze Wang et al.’s protocol in detail. In addition, we propose an improvement to avoid the information leakage. The security of the improved protocol has also been discussed.