Sharp finite statistics for minimum data block sizes in quantum key distribution

• URL: http://arxiv.org/abs/2410.04095v1
• Date: Sat, 5 Oct 2024 09:30:55 GMT
• Title: Sharp finite statistics for minimum data block sizes in quantum key distribution
• Authors: Vaisakh Mannalath, Víctor Zapatero, Marcos Curty,
• Abstract summary: We introduce an alternative solution that exploits a link between random sampling with and without replacement. Despite its simplicity, it notably boosts the achievable secret key rate. Bounds of this kind naturally fit in finite-key security proofs of decoy-state QKD schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The performance of quantum key distribution (QKD) heavily depends on the finite statistics of its security proof. For multiple protocols and proof techniques, the central statistical task is a random sampling problem, which is customarily addressed by invoking suitable tail bounds on the hypergeometric distribution. In this work, we introduce an alternative solution that exploits a link between random sampling with and without replacement. Despite its simplicity, it notably boosts the achievable secret key rate, particularly in the regime of small data block sizes critical for satellite QKD and other envisioned QKD applications. Moreover, as a by-product of the proposed tool, tight Neyman constructions are derived for the average of independent Bernoulli variables. Bounds of this kind naturally fit in finite-key security proofs of decoy-state QKD schemes, further sharpening the finite statistics compared to previous approaches.

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