  Detection-efficiency mismatch is a common problem in practical quantum key
distribution (QKD) systems. Current security proofs of QKD with
detection-efficiency mismatch rely either on the assumption of the
single-photon light source on the sender side or on the assumption of the
single-photon input of the receiver side. These assumptions impose restrictions
on the class of possible eavesdropping strategies. Here we present a rigorous
security proof without these assumptions and, thus, solve this important
problem and prove the security of QKD with detection-efficiency mismatch
against general attacks (in the asymptotic regime). In particular, we adapt the
decoy state method to the case of detection-efficiency mismatch.
