发表机构
Thales; Institut Polytechnique de Paris; EURECOM; Lab-STICC, UMR CNRS 6285, ENSTA, Institut Polytechnique de Paris; Univ. Brest, CNRS, Lab-STICC UMR 6285（泰雷兹; 巴黎理工学院; 欧洲通信管理高等学院; 巴黎理工学院 ENSTA，CNRS 6285 Lab-STICC 联合实验室; 布雷斯特大学，CNRS，Lab-STICC 联合实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究两种四量子比特CSS量子纠错码在水下BB84 QKD中的影响，通过信道模型和QBER/SKR分析，发现QECC仅在边际信噪比下有益，可扩展工作深度范围，但高信噪比时原始BB84更优。
AI 中文摘要
量子密钥分发（QKD）能够实现海事基础设施所必需的安全水下通信。水下光信道会引入大量的光子损失（擦除）和环境噪声，从而降低QKD的性能。本文研究了两种四量子比特Calderbank-Shor-Steane（CSS）量子纠错码（QECC）是否能减轻垂直水下通信BB84 QKD协议中的这些损害。在开发了一个包含光子损失、几何扩展和太阳噪声的综合随机信道模型之后，我们通过解析研究量子比特误码率（QBER）和有无安全情况下的安全密钥率（SKR）随信噪比（SNR）的变化来评估QECC的可行性，并通过蒙特卡洛模拟进行了验证。标准的四量子比特CSS码在QBER为11%的安全阈值处实现了3 dB的SNR增益；丢弃码变体实现了4.5 dB的增益。然而，QECC包含编码开销，降低了SKR。我们证明了SKR与发送光子到达概率之间的关键关系。分析表明，QECC仅在边际SNR区域有益；在高SNR下，原始BB84占主导地位。对于海洋III型Jerlov水体场景，太阳位于大气层顶部，我们确定了QECC能够实现原本不可行的通信的可行深度范围窗口。该分析确立了纠错部署必须依赖于场景：在SNR边际时，以吞吐量为代价扩展工作范围，或在SNR高时优先考虑密钥生成速率。
英文摘要
Quantum key distribution (QKD) enables secure underwater communications essential for maritime infrastructure. Underwater optical channels introduce substantial photon loss (erasures) and ambient noise that degrade QKD performance. This paper investigates whether two four-qubit Calderbank-Shor-Steane (CSS) quantum error correction codes (QECC) mitigate these impairments in vertical underwater communication BB84 QKD protocol. After developing a comprehensive stochastic channel model incorporating photon loss, geometric spreading, and solar noise, we assess the viability of QECC through the analytical study of the quantum bit error rate (QBER) and the secure key rate (SKR) with and without security depending on the signal-to-noise ratio (SNR) validated against Monte Carlo simulations. The standard four-qubit CSS code achieves a 3 dB SNR gain at the QBER 11% security threshold; the discard code variant achieves 4.5 dB. However, QECC includes an encoding overhead that reduces the SKR. We demonstrate a crucial relationship between the SKR and the probability of arrival of the sent photon. Analysis shows that QECC is beneficial exclusively in marginal SNR regimes; at high SNR, raw BB84 dominates. For an ocean Type III Jerlov water scenario with sunlight coming from the sun located at the top of the atmosphere, we identify operational depth-range windows where QECC enables communication otherwise infeasible. This analysis establishes that error correction deployment must be scenario-dependent: extend operational range at the cost of throughput when SNR is marginal, or prioritize key generation rates at high SNR.
Comments37 pages, 13 figures
