Security analysis of measurement-device-independent quantum secure direct communication

Quantum secure direct communication (QSDC) is an important branch of quantum communication that transmits confidential messages directly in a quantum channel without utilizing encryption and decryption. It not only prevents eavesdropping during transmission, but also eliminates the security loophole associated with key storage and management. Recently measurement-device-independent (MDI) QSDC protocols in which the measurement is performed by an untrusted party using imperfect measurement devices have been constructed, and MDI-QSDC eliminates the security loopholes originating from the imperfections in measurement devices so that enable applications of QSDC with current technology. In this paper, we complete the quantitative security analysis of the MDI-QSDC protocols, one based on EPR pairs and one based on single photons. In passing, a security loophole in one of the MDI-QSDC protocols (Niu et al. in Sci Bull 63(20):1345-1350, 2018) is fixed. The security capacity is derived, and its lower bound is given. It is found that the MDI-QSDC secrecy capacity is only slightly lower than that of QSDC utilizing perfect measurement devices. Therefore, QSDC is possible with current measurement devices by sacrificing a small amount in the capacity.