Improved finite-size effects in QKD protocols with applications to decoy-state QKD

TL;DR

This paper develops a tighter finite-size security proof for quantum key distribution protocols, including decoy-state BB84, improving key rate estimates and extending security to coherent attacks and practical imperfections.

Contribution

It introduces refined concentration inequalities and second-order correction improvements, enhancing finite-size key rate calculations and security proofs for practical QKD protocols.

Findings

Tighter finite-size key rates achieved with refined inequalities.

Extended security proof to coherent attacks and variable-length protocols.

Applied results to decoy-state BB84 with practical imperfections.

Abstract

We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks and extend it to coherent attacks using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter finite-size key rates by employing refined concentration inequalities in the acceptance testing phase. Second, we improve second-order correction terms in the key rate expression, by reducing them to scale with the number of sifted rounds rather than the total number of protocol rounds. We apply these advancements to compute finite-size key rates for a qubit and decoy-state BB84 protocol, accommodating arbitrary protocol parameters. Finally, we extend our finite-size security proof to coherent attacks and variable-length protocols and present our results for the decoy-state 4-6 protocol incorporating imperfections such as unequal intensity settings.