发表机构
Leibniz Universität Hannover（汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过二元估计和测量χ²散度，连接熵信道序与私有容量，解释零私有容量信道的激活现象，并确定Werner-Holevo信道的私有容量阈值。
AI 中文摘要
最近的例子表明，零私有容量并不必然意味着反退化性，并且两个零私有容量的信道联合起来仍然可以传输私有信息。现有的熵信道序比较接收者及其环境能学到什么，从而对容量进行界定。我们将这些序与通过二元估计的最新构造联系起来，二元估计的最小均方误差由测量的χ²散度控制。一个新的积分表示表明，在量子比特扩展上的测量χ²如何恢复量子χ²。它使我们能够从完全的测量χ²序过渡到完全的量子χ²、相对熵和更少噪声序。Zhu和Wang使用符号提升来表明他们的qutrit信道具有零私有容量。我们证明，Hermitian平滑的测量χ²序刻画了此类提升存在的条件，即使有量子参考也是如此。在每个块长度上的二元估计中的环境优势产生了有限码可靠性-保密性界。这些结果解释了为什么完全比较可以防止与反退化辅助体的激活，而仅正则化比较则不能。基于该qutrit示例，我们为一系列噪声Werner-Holevo信道建立了这种稳定性，确定了尖锐的私有容量和反退化阈值，并在非退化范围内计算了精确的互补容量。相比之下，我们将Pauli半擦除激活扩展到所有1/2≤p<1，并为一个新的四能级族建立了相同的范围。参考辅助的测量χ²见证者解释了为什么这些激活构造缺乏完全比较。
英文摘要
Recent examples have shown that zero private capacity need not imply antidegradability and that two channels with zero private capacity can nevertheless transmit private information together. Existing entropic channel orders compare what a receiver and its environment can learn and thereby bound capacities. We connect these orders to the recent constructions through binary estimation, whose minimum mean-square error is governed by measured $χ^2$ divergence. A new integral representation shows how measured $χ^2$ on a qubit extension recovers quantum $χ^2$. It lets us pass from complete measured-$χ^2$ ordering to complete quantum-$χ^2$, relative-entropy, and less-noisy ordering. Zhu and Wang used a signed lift to show that their qutrit channel has zero private capacity. We show that Hermitian-smoothed measured-$χ^2$ ordering characterizes when such lifts exist, even with a quantum reference. Environmental dominance in binary estimation at every blocklength yields a finite-code reliability--secrecy bound. These results explain why complete comparison prevents activation with antidegradable helpers whereas regularized comparison alone does not. Building on that qutrit example, we establish this stability for a range of noisy Werner--Holevo channels, determine sharp private-capacity and antidegradability thresholds, and compute exact complementary capacities in a nondegradable range. By contrast, we extend Pauli half-erasure activation to all $1/2\le p<1$ and establish the same range for a new four-level family. Reference-assisted measured-$χ^2$ witnesses show why these activating constructions lack complete comparison.
Comments40 pages
