The finite key effect of side-channel-secure quantum key distribution beyond post-selection technique

Practical quantum key distribution (QKD) systems often face vulnerabilities due to hardware imperfections, such as side-channel attacks on the source. While the side-channel-secure (SCS) protocol provides a defense, existing finite-key security proofs often rely on post-selection techniques that are highly sensitive to the total number of pulses, leading to inefficient key rates. This paper seeks to derive a more efficient, direct security proof for the SCS protocol against coherent attacks without relying on post-selection.

The authors utilize the framework of the Entropic Uncertainty Relation (EUR) and the Quantum Leftover Hash Lemma (QLHL) to reframe composable security as a statistical fluctuation problem of phase errors. By modifying the SCS protocol to randomly divide bits into two independent subsets, they enable the use of virtual observables to estimate phase errors. A key innovation is the proof that Alice and Bob can perform error correction first and then compute the final secure key length based on the actual information leakage observed during the reconciliation process, rather than relying on pre-determined bounds.

The proposed method yields tighter key rates for the SCS protocol and reduces the required number of pulses by over two orders of magnitude compared to previous post-selection-based approaches. The authors establish that for protocols where untagged bits are bit-error-free, the final key length can be determined adaptively after error correction. They further provide sufficient conditions for applying this post-error-correction calculation to a broader class of QKD protocols, enhancing the practical utility of variable-length QKD implementations.

This work bridges the gap between theoretical security proofs and practical engineering practices in QKD. By allowing the use of actual error-correction leakage in key-rate formulas, the protocol becomes more robust and efficient in real-world scenarios where channel behavior is not known in advance. This advancement simplifies the security justification for practical variable-length QKD systems while maintaining rigorous composable security against coherent attacks.