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Semi-device-independent quantum key distribution(SDI-QKD) has been proposed by applying the quantum dimension correlation, and the security relies on the violation of quantum dimension witness inequalities. We prove the security of the SDI-QKD protocol under the depolarization channel by considering the quantum dimension witness inequalities and minimum entropy and the specific process of the QKD protocol, combining with a fourquantum-state preparation and three measurement bases. We also provide the relationship between the dimension witness value, the error rate and the security key rate by the numerical simulation.
Semi-device-independent quantum key distribution (SDI-QKD) has been proposed by applying the quantum dimension correlation, and the security relies on the violation of quantum dimension witness inequalities. We prove the security of the SDI-QKD protocol under the depolarization channel by considering the quantum dimension witness inequalities and minimum entropy and the specific process of the QKD protocol, combining with a four quantum-state preparation and three measurement bases. We also provide the relationship between the dimension witness value, the error rate and the security key rate by the numerical simulation.