Optimizing Epsilon Security Parameters in QKD

We investigate the optimization of epsilon-security parameters in quantum key distribution (QKD), aiming to improve the achievable secure key rate under a fixed overall composable security level. For this purpose, we employ a continuous genetic algorithm (CGA) to optimize the epsilon-security components of two representative protocols: the homodyne protocol from the continuous-variable (CV) family and the BB84 protocol from the discrete-variable (DV) family. We detail the CGA configuration, summarize the derivation of the composable key rate, and emphasize the role of the epsilon-parameters in both protocols. We then compare key rates obtained with optimized epsilon-values against those derived from standard and randomized choices. Our results demonstrate substantial key rate improvements at high security levels, where the key rate typically vanishes, and uncover positive-rate regimes that are inaccessible without optimization.

💡 Research Summary

The paper investigates how to allocate the components of the overall ε‑security budget in quantum key distribution (QKD) in order to maximize the achievable secret key rate under a fixed composable security level. The authors focus on two representative protocols: a continuous‑variable (CV) homodyne protocol and the discrete‑variable BB84 protocol. In both cases the total ε‑security can be decomposed into several error contributions: parameter‑estimation error (ε_PE), entropy‑estimation error (ε_ent, present only in CV), correctness error (ε_cor), smoothing error (ε_s) and hashing error (ε_h). The secrecy error is defined as ε_sec = ε_s + ε_h. For CV‑QKD the total security budget satisfies ε = 3 ε_PE + ε_cor + ε_sec (the factor 3 accounts for the estimation of two channel parameters), while for BB84 it reduces to ε = ε_PE + ε_cor + ε_sec.

The authors treat ε_PE and ε_cor as the free variables to be optimized, reconstructing ε_sec from the fixed total ε via the linear constraint. This reduces the dimensionality of the search space to two continuous variables. To perform the optimization they employ a Continuous Genetic Algorithm (CGA), an evolutionary method that works directly with real‑valued chromosomes. Each chromosome consists of two normalized genes p₁, p₂ ∈