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 A1 and A2. (+) 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