Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.

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• Quantum cryptography