编码TE-QKD信道中的多样性：利用有限系统资源实现无限多样性
Diversity in Coded TE-QKD Channels: Achieving Infinite Diversity out of Finite System Resources
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中文总结 AI 辅助
本文研究编码TE-QKD协商的多样性阶，证明在信道和码长有限时，通过特定条件可实现无限多样性，相关短码示例验证了分析结果。
中文摘要 AI 辅助
本文针对时间-纠缠量子密钥分发（TE-QKD）的协商过程，建立了纠错码实现无限多样性的条件并给出证明。该研究得出了编码与通信理论文献中从未出现过的惊人结果：即使信道具有有限多样性且码长相对较短，译码器仍能展现出无限多样性阶。本文研究编码TE-QKD协商的多样性阶，其定义为高信噪比下误码概率的渐近斜率。对于有界距离代数译码，我们根据每个码字的光子数和译码半径推导了充要条件；对于软判决译码，我们引入了最大有限多样性（MFD）特性，并证明当且仅当码为MFD缺陷码时可实现无限多样性。TE-QKD中的无限多样性在经典衰落信道中并无对应情况，经典衰落信道中译码仅能将有限多样性阶乘以有限因子。基于Golay码、里德-所罗门（Reed-Solomon）码、Bose-Chaudhuri-Hocquenghem（BCH）码和里德-穆勒（Reed-Muller）码的短码示例验证了该分析，并阐明了TE-QKD系统参数及相对较短的码参数如何影响硬信息和软信息协商的可实现多样性。
英文摘要
We establish conditions and give proofs on how an error-correcting code can attain infinite diversity in a time-entanglement quantum key distribution (TE-QKD) reconciliation. The shocking result, never encountered in the literature on coding and communication theory, is that a decoder exhibits an infinite diversity order while the channel has finite diversity and the code has a relatively short finite length. This paper studies the diversity order of coded TE-QKD reconciliation, defined by the asymptotic slope of the error probability at high signal-to-noise ratio. For bounded-distance algebraic decoding, we derive a necessary and sufficient condition in terms of the number of photons per codeword and the decoding radius. For soft-decision decoding, we introduce the maximal finite diversity (MFD) property and prove that infinite diversity is achieved if and only if the code is MFD deficient. The infinite diversity in TE-QKD has no counterpart in classical fading channels, where decoding can only multiply a finite diversity order by a finite factor. Examples of short codes based on Golay, Reed-Solomon, Bose-Chaudhuri-Hocquenghem (BCH), and Reed-Muller codes validate the analysis and illustrate how the TE-QKD system parameters and the relatively short code parameters affect the achievable diversity for both hard and soft information reconciliation.
