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The decoy-state method is a standard enhancement to quantum key distribution(QKD) protocols that has enabled countless QKD experiments with inexpensivelight sources. However, new technological advancements might require furthertheoretical study of this technique. In particular, the decoy-state method istypically described under the assumption of a Poisson statistical distributionfor the number of photons in each QKD pulse. This is a practical choice,because prepare-and-measure QKD is often implemented with attenuated lasers,which produce exactly this distribution. However, sources that do not meet thisassumption are not guaranteed to be compatible with decoy states. In this work,we provide security bounds for decoy-state QKD using a source with an arbitraryphoton emission statistic. We consider both the asymptotic limit of infinitekey and the finite-size scenario, and evaluate two common decoy-state schemes:the vacuum+weak and one-decoy protocols. We numerically evaluate theperformance of the bounds, comparing three realistic statistical distributions(Poisson, thermal, binomial), showing that they are all viable options for QKD.

Security bounds for decoy-state QKD with arbitrary photon-number statistics