AI 中文总结
研究高斯调制连续变量量子密钥分发中不可检测参数估计攻击的信息论极限，将边信道检测形式化为证书伪造假设检验，证明二分法，给出证书可重用率及有限大小密钥长度陈述，结果在特定条件下成立。
AI 中文摘要
我们将高斯调制连续变量量子密钥分发（CV-QKD）中的边信道检测形式化为证书伪造假设检验，并用信息论速率来确定其可检测性。相对于一组可信的、实时监测的可观测量集合$\mathcal{M}$，良性统计证书的伪造可检测率$g_{\mathcal{M}}$是漏检的斯坦指数。我们证明了一个二分法：当散粒噪声单位可信时，$g_{\mathcal{M}}$在泄漏的霍列沃信息中是单调且严格正的，否则恒为零，恢复了局部振荡器和校准攻击作为退化情况。单调性通过非渐近界$\varepsilon_{\mathrm{PE}}\le\exp(-N_{\mathrm{PE}}\psi(r))$产生了证书可重用率，该界限制了在$N_{\mathrm{PE}}$次估计轮次中与未检测到的证书兼容的霍列沃泄漏，其近阈值展开与标准有限大小分析的高斯置信区间缩放相匹配。然后，我们在集体高斯攻击下给出了一个可组合的有限大小密钥长度陈述，其最坏情况下的霍列沃项是可重用率，并且其参数估计失败概率在每个块长度上由斯坦指数界定。这两个结果在可信相关模型中是无条件的，在该模型中，过量噪声中霍列沃泄漏的严格单调性来自于噪声注入论证；对于一般的$\mathcal{M}$，它们在关于散度景观的明确无虚假局部极小值条件下成立，可通过低维检查验证。速率的凸性进一步假设了霍列沃界的数值支持的凹性，这是唯一的数值成分；整个证明状态都有界定。
英文摘要
We formalize side-channel detection in Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) as a certificate-forgery hypothesis test and identify its detectability with an information-theoretic rate. Relative to a set $\mathcal{M}$ of trusted, real-time-monitored observables, the forgery- detectability rate $g_{\mathcal M}$ of a benign-statistics certificate is the missed-detection Stein exponent. We prove a dichotomy: $g_{\mathcal M}$ is monotone and strictly positive in the leaked Holevo information when the shot- noise unit is trusted, and identically zero otherwise, recovering local- oscillator and calibration attacks as the degenerate case. Monotonicity yields a certificate reusability rate bounding the Holevo leakage compatible with an undetected certificate over $N_{\mathrm{PE}}$ estimation rounds, via the non- asymptotic bound $\varepsilon_{\mathrm{PE}}\le\exp(-N_{\mathrm{PE}}ψ(r))$ whose near-threshold expansion matches the Gaussian confidence-interval scaling of standard finite-size analyses. We then give a composable finite-size key- length statement under collective Gaussian attacks, whose worst-case Holevo term is the reusability rate and whose parameter-estimation failure probability is bounded by the Stein exponent at every block length. Both results are unconditional in the trusted-correlation model, where strict monotonicity of the Holevo leakage in the excess noise follows from a noise-injection argument; for general $\mathcal{M}$ they hold under an explicit no-spurious-local-minima condition on the divergence landscape, verifiable by low-dimensional inspection. Convexity of the rate further assumes a numerically supported concavity of the Holevo bound, the sole numerical ingredient; proof status is delimited throughout.
Comments12 pages, 11 figures
