Security proof of practical quantum key distribution schemes
  This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation. To prove the security, it is not assumed that defects in the devices are absorbed into an adversary's attack. In fact, the only assumption in the proof is that the source is characterized. The proof is performed by lower-bounding adversary's Renyi entropy about the key before privacy amplification. The bound reveals the leading factors reducing the key generation rate. 
Yodai Watanabe