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.
However, security proofs which take into account certain imperfection of hardware devices are still challenging. One of such imperfections is so called detection-efficiency mismatch, where two single-photon detectors have different quantum efficiencies, i.e., different probabilities of photon detection. Such a problem should be taken into account because it is practically impossible to make two absolutely identical detectors.
Mathematically, security proof for QKD with detection-efficiency mismatch for the general case is challenging because the Hilbert space we deal with is infinite-dimensional (a reduction to a finite-dimensional space that is possible for the case of identical detectors does not work here). So, fundamentally new approaches to prove the security was required. The main new method proposed in this work is an analytical bound of the number of multiphoton detection events using the entropic uncertainty relations. This allows us to reduce the problem to a finite-dimensional one. For the analytical solution of the finite-dimensional problem (which is still non-trivial), we propose to use symmetries of the problem.
Thus, in this paper, we proof the security of the BB84 protocol with detection-efficiency mismatch and analytically derive bounds for the secret key rate in this case. Also we adapt the decoy state method to the case of detection-efficiency mismatch.
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