Finite-key security analysis for quantum key distribution with leaky sources

Security proofs of quantum key distribution (QKD) typically assume that the devices of the legitimate users are perfectly shielded from the eavesdropper. This assumption is, however, very hard to meet in practice, and thus the security of current QKD implementations is not guaranteed. Here, we fill this gap by providing a finite-key security analysis for QKD which is valid against arbitrary information leakage from the state preparation process of the legitimate users. For this, we extend the techniques introduced by Tamaki et al (2016 New J. Phys. 18 065008) to the finite-key regime, and we evaluate the security of a leaky decoy-state BB84 protocol with biased basis choice, which is one of the most implemented QKD schemes today. Our simulation results demonstrate the practicability of QKD over long distances and within a reasonable time frame given that the legitimate users' devices are sufficiently isolated.