## 5 Conclusions and Discussions  
This work investigates an effective approach to QKD post-processing algorithms by focusing on rate-adaptive reconciliation and its integration with syndrome-based error estimation and polynomial-based hash subblock confirmation. By utilizing syndrome-based estimation, this approach significantly improves the accuracy and minimizes the variability of the estimated QBER value. It enables rate-adaptive reconciliation to effectively determine the optimal code rate, consequently reducing the number of communication rounds in practice. Simulation results demonstrate that this unified approach requires fewer information leakages, improves the reconciliation efficiency, and ensures the integrity of identical keys. These findings clearly indicate that the proposed approach can greatly enhance the efficiency of classical post-processing, achieving higher secret key throughput over longer transmission distances.  
In QKD post-processing, the amount of information leakage during information reconciliation significantly influences the efficiency of classical post-processing. These leakages are subsequently eliminated in the privacy amplification, which directly reduces the final secret key size, according to the information-theoretic security principles. Efficient information reconciliation based on irregular LDPC codes with large block lengths of up to \(10^{5}\) bits offers superior error-correction capability. This allows for setting the baseline efficiency metric close to the theoretical limit, thereby minimizing the generation of syndrome information, which constitutes the information leakage in practice. Furthermore, the use of an extensive amount of punctured and shortened bits can degrade the error-correction capability of the original code design. To address this issue, this work employs the standard LDPC codes from [36; 37] for a set of original code rates, arranged in a sequence from a high to low rate, with each rate closely spaced. This approach minimized the total number of puncturing and shortening bits, enabling efficient adaptation of the original code rate while maintaining robust error-correction capability for realizing the optimal efficiency of classical post-processing.  
In future work, the unified approach of the proposed schemes will be analyzed within the context of finite key security to comprehensively assess the overall security parameters. Additionally, this approach will be applied to practical QKD systems, enabling higher-speed QKD applications.  
Conceptualization, P.T.; Methodology, P.T.; Software, P.T.; Validation, P.T. and C.-M.Z.; Formal Analysis, P.T.; Investigation, P.T. and C.-M.Z.; Resources, P.T. and C.-M.Z.; Data curation, P.T. and C.-M.Z.; Writing-Original Draft Preparation, P.T.; Writing-Review & Editing, P.T. and C.-M.Z.; Visualization, P.T.; Supervision, P.T.; Project Administration, P.T.; Funding Acquisition, P.T. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Research Fund of Phranakhon Rajabhat University (PNRU), Bangkok, Thailand (Grant Number: 3/2023).  
Not applicable.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & **Efficiency of BB84** & **Efficiency of Single-Photon Detector (\(\epsilon_{\text{detect}}\))** & **Dark Count Probability of Single-Photon Detector (\(p_{dark}\))** & **Optical Fiber Losses (dB/km)** \\ \hline
**Value** & 0.5 & 0.1 & \(10^{-5}\) & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of a BB84 QKD setup based on the inherent properties of the single photon source and detection, as well as the optical fiber losses of the quantum channel.