Abstract
Quantum key distribution (QKD) protocols with threshold detectors are driving high-performance QKD demonstrations. The corresponding security proofs usually assume that all physical detectors have the same detection efficiency. However, the efficiencies of the detectors used in practice might show a mismatch depending on the manufacturing and setup of these detectors. A mismatch can also be induced as the different spatial-temporal modes of an incoming signal might couple differently to a detector. Here we develop a method that allows to provide security proofs without the usual assumption. Our method can take the detection-efficiency mismatch into account without having to restrict the attack strategy of the adversary. Especially, we do not rely on any photon-number cut-off of incoming signals such that our security proof is directly applicable to practical situations. We illustrate our method for a receiver that is designed for polarization encoding and is sensitive to a number of spatial-temporal modes. In our detector model, the absence of quantum interference between any pair of spatial-temporal modes is assumed. For a QKD protocol with this detector model, we can perform a security proof with characterized efficiency mismatch and without photon-number cut-off assumption. Our method also shows that in the absence of efficiency mismatch in our detector model, the key rate increases if the loss due to detection inefficiency is assumed to be outside of the adversary's control, as compared to the view where for a security proof this loss is attributed to the action of the adversary.
Highlights
For practical quantum key distribution (QKD) [1] using photon-counting techniques, information is usually encoded in optical signals that contain multiple photons
We remark that the numerical method developed in Ref. [19] obtains a key-rate lower bound by the following two steps: First, by an iterative method, we find a near-optimal solution of the convex-optimization problem in Eq (2) and an upper bound on the privacy amplification (PA) term α; second, we take advantage of the duality principle satisfied by convex optimization to obtain a reliable lower bound β on the PA term α
The security proof of QKD usually assumes that the threshold detectors used have the same detection efficiency
Summary
For practical quantum key distribution (QKD) [1] using photon-counting techniques (discrete variable QKD), information is usually encoded in optical signals that contain multiple photons. Security proofs of practical QKD protocols usually assume that all threshold detectors used have the same efficiency. [10,11,12,13] studied the security proof of the BB84-QKD protocol in the presence of efficiency mismatch but under the assumption that Bob receives no more than one photon at each round. This assumption cannot be justified in practical implementations of QKD where threshold detectors are being used. We note that all detectors considered in the rest of the paper are threshold detectors by default
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