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.

量子安全直接通信（QSDC）是量子通信的重要分支，它可以直接在量子通道中传输机密消息，而无需利用加密和解密。它不仅防止了传输过程中的窃听，而且还消除了与密钥存储和管理相关的安全漏洞。最近，已经构建了与测量设备无关（MDI）的QSDC协议，其中不可信方使用不完善的测量设备执行测量，并且MDI-QSDC消除了源自测量设备不完善之处的安全漏洞，从而使QSDC的应用成为可能用当前的技术。在本文中，我们完成了MDI-QSDC协议的定量安全性分析，一种基于EPR对，另一种基于单光子。顺便，MDI-QSDC协议之一（Niu等人在Sci Bull 63（20）：1345-1350，2018年）中的安全漏洞已得到修复。推导安全能力，并给出其下限。结果发现，MDI-QSDC的保密能力仅比使用完善的测量设备的QSDC的保密能力低。因此，通过牺牲少量的容量，可以在电流测量装置中实现QSDC。