发表机构
School of Data Science, The Chinese University of Hong Kong, Shenzhen; International Quantum Academy; Graduate School of Mathematics, Nagoya University; Dahlem Center for Complex Quantum Systems, Freie Universität Berlin; Perimeter Institute for Theoretical Physics; Institute for Quantum Computing, University of Waterloo（香港中文大学（深圳）数据科学学院; 国际量子学院; 名古屋大学大学院数学研究科; 柏林自由大学达勒姆复杂量子系统中心; 理论物理珀米特研究所; 滑铁卢大学量子计算研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对协变经典-量子窃听信道，利用酉群轨道结构构造有限块预处理方案，以熵差表征私有信息，并通过数值优化证明在混合二进制信道上可超越噪声重复基准，且验证了非可加性。
AI 中文摘要
对于具有传递协变输入作用的经典-量子窃听信道，两个输出系综均可描述为固定种子态在酉群轨道上的形式。我们利用这一结构构造了有限块预处理方案，其私有信息是在两个通过群卷积相关联的分布上求得的熵差。将该构造应用于乘积群，可以处理任意固定次数的信道使用之间的相关性。我们给出了相关均匀输入界等于单次使用私有信息的充分条件。常数组合信道码和universal$_2$哈希可实现所得速率，其迹距离泄漏由夹层Rényi信息控制。对于均匀外部随机化，表示结构将比较态优化简化为Eve的不变态。对于Tikku、Berta和Renes考虑的混合二进制信道，在三次和四次使用时的数值优化给出的速率，在我们测试网格上该估计为正的所有点上，均高于我们对优化噪声重复基准的数值估计。改进来源于独立物理翻转族之外的噪声分布以及对称逻辑翻转。我们还利用两次使用编码器、解析的单次使用逆界和认证熵界，在显式信道参数下证明了非可加性。最后，我们将混合模型与固定接收机测量下的二进制相移键控联系起来。
英文摘要
For classical--quantum wiretap channels with a transitive covariant input action, both output ensembles admit a description as unitary group orbits of fixed seed states. We use this structure to construct finite-block preprocessing schemes whose private information is an entropy difference evaluated at two distributions related by group convolution. Applying the construction to product groups allows correlations across any fixed number of channel uses. We give a sufficient condition for the associated uniform-input bound to equal the single-use private information. Constant-composition channel codes and universal$_2$ hashing achieve the resulting rates, with trace-distance leakage controlled by sandwiched Rényi information. For uniform outer randomization, the representation structure reduces the comparison-state optimization to Eve's invariant states. For the hybrid binary channel considered by Tikku, Berta and Renes, numerical optimization at three and four uses gives rates above our numerical estimate of the optimized noisy-repetition benchmark wherever that estimate is positive on the tested grid. The improvement comes from noise distributions beyond the family of independent physical flips and a symmetric logical flip. We also prove nonadditivity at an explicit channel parameter using a two-use encoder, an analytic single-use converse, and certified entropy bounds. Finally, we relate the hybrid model to binary phase-shift keying with a fixed receiver measurement.
