条件压缩系数及其在量子网络中的应用
Conditional contraction coefficients and their applications to quantum networks
AI总结：
本研究引入条件压缩系数框架，将经典相对熵与互信息压缩的对应关系扩展至量子边信息场景，为量子网络信息压缩分析提供统一框架，并拓展了相关边界与极限。
AI中文摘要：
压缩系数量化了信道引起的可区分性损失，为数据处理不等式提供了强形式。标准压缩系数忽略辅助量子系统，现有基于完全压缩系数的扩展则要求被比较态具有相同的参考边缘分布。本研究引入条件压缩系数，这一新颖家族通过减去参考系统中已存在的可区分性，纳入任意量子参考系统。我们开发了具备此类量子边信息的压缩系数通用框架，包括对应的强数据处理不等式（SDPI）常数、扩展系数及相对压缩系数。对于迹距离，我们证明优化可被限制在正交输入态；对于量子相对熵，我们证明其条件压缩系数恰好等于条件互信息的压缩系数，将相对熵压缩与互信息压缩间的经典对应关系扩展至量子边信息场景。更一般地，我们确定了这些结果所需的散度结构性质，并讨论了相对熵之外的扩展。这些结果建立了用于分析量子网络场景中信息压缩的统一框架，其中量子边信息与分布式关联是信息处理任务的固有特征。应用包括Polyanskiy-Wu互信息压缩边界的扩展、混合时间的新视角，以及量子存储器的基本极限。
英文摘要：
Contraction coefficients quantify the loss of distinguishability induced by a channel and provide a strong form of the data-processing inequality. While standard contraction coefficients ignore auxiliary quantum systems, existing extensions based on complete contraction coefficients require the compared states to have identical reference marginals. In this work, we introduce conditional contraction coefficients, a novel family that incorporates arbitrary quantum reference systems by subtracting the distinguishability already present in the reference system. We develop a general framework for contraction coefficients with such quantum side information, including the corresponding strong-data-processing-inequality (SDPI) constants, expansion coefficients, and relative contraction coefficients. For the trace distance, we show that the optimization can be restricted to orthogonal input states. For the quantum relative entropy, we prove that its conditional contraction coefficient is exactly equal to the contraction coefficient of the conditional mutual information, extending the classical correspondence between relative-entropy contraction and mutual-information contraction to the setting with quantum side information. More generally, we identify structural properties of divergences required for these results and discuss extensions beyond the relative entropy. These results establish a unified framework for analyzing information contraction in quantum network settings, where quantum side information and distributed correlations are intrinsic features of the information-processing task. Applications include an extension of the Polyanskiy-Wu bounds on mutual information contraction, new perspectives on mixing times, and fundamental limits on quantum memories.
