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We propose two quantum key distribution (QKD) protocols based on Bell'sinequality, which can be considered as modified time-reversed E91 protocol.Similar to the measurement-device-independent quantum key distribution(MDI-QKD) protocol, the first scheme requires the assumption that Alice and Bobperfectly characterize the encoded quantum states. However, our second protocoldoes not require this assumption, which can defeat more known and unknownsource-side attacks compared with the MDI-QKD. The two protocols are naturallyimmune to all hacking attacks with respect to detections. Therefore, thesecurity of the two protocols can be proven based on the violation of Bell'sinequality with measurement data under fair-sampling assumption. In oursimulation, the results of both protocols show that long-distance quantum keydistribution over 200 km remains secure with conventional lasers in theasymptotic-data case. We present a new technique to estimate the Bell'sinequality violation, which can also be applied to other fields of quantuminformation processing.

Measurement-device-independent quantum key distribution based on Bell's inequality