Fig. 1. Measuring process of proposed MDI-QSDC. A, B, C, and D are logical qubits. Circles with numeric subscripts represent physical particles. For example, the logical particle A is composed of $A_{\mathrm{1}}$ and $A_{\mathrm{2}}$. (+) and (×) stand for decoy qubits constructed by single photons in Z-basis and X-basis. Photons framed together represent combination of particles to be performed Bell measurement

Fig. 2. Communication process of proposed MDI-QSDC. Circles surrounded by dotted lines represent logical particles. (+), (×) stand for decoy photons. In step 4), photons labeled “check” are used for security check. Photons labeled “discard” mean case of discarding. Remaining ones are for coding message

Table 1. Effects for measurement of different combinations in communication process of role