Entanglement-based quantum key distribution with untrusted third party

In quantum key distribution, it is important to ensure the secure key rate and the distribution distance. To increasing transmission distance, we propose an entanglement-based protocol relying on two Bell states. Combining the idea of remote state preparation, the protocol can double the communication distance without introducing more security loopholes related to measurement device, and maintain the key generation rate consistent with the BBM92 protocol via untrusted third party. Based on that, we investigate key rate of the protocol when transmitted qubits are subjected to four noises. The result shows that our protocol can tolerate more amplitude damping noise than ES−BBM92 protocol. In addition, we found that if noise is unavoidable and the noise parameter exceeds a certain value, in some noisy environments, it is best to subject qubit to more noise to increase the secret key generation rate. Furthermore, we calculate secret key rate under both practical experimental condition and noisy environment.