Security of the traditional quantum key distribution protocols with finite-key lengths

Quantum key distribution (QKD) in principle can provide unconditional secure communication between distant parts. However, when finite-key length is taken into account, the security can only be ensured within certain security level. In this paper, we adopt the Chernoff bound analysis method to deal with finite-key-size effects, carrying out corresponding investigations on the relationship between the key generation rate and security parameters for different protocols, including BB84, measurement-device-independent and twin-field QKD protocols. Simulation results show that there exists a fundamental limit between the key rate and the security parameters. Therefore, this study can provide valuable references for practical application of QKD, getting a nice balance between the key generation rate and the security level.