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There is considerable interest in predicting the efficiency of Quantum KeyDistribution (QKD) protocols when one of their implementation quantities ismodified. One significant imperfection that affects the efficiency of the setupis the afterpulse phenomenon which consists in the spontaneous detectionstriggered by trapped carriers after previous avalanches at the detectors. Whileit is widely studied in bibliography for various QKD protocols, it has beenreported much more scarcely for the well-known decoy-state QKD protocols andfor dual detectors only. We develop a theoretical analysis of afterpulsingeffect on the decoy-state QKD protocols for multiple detectors, deliveringresults which can be used as a guide for every practical decoy-state QKDprotocol implementation in real-world deployments. A new formula connecting thebaseline system error rate and the afterpulse probability is derived which mayhold for all protocols as it is consisted of only setup-related quantities.Numerical simulations addressing the significance of breaking down thequantities pertaining to the decoy-state QKD protocols are being made, focusingon the weak+vacuum decoy-state QKD protocol as a characteristic subcase.

Afterpulsing Effect on the Baseline System Error Rate and on the Decoy-State Quantum Key Distribution Protocols