标题： 量子相干性的熵图表征：退化浓缩和最大本征值不确定性界限 显示英文标题

标题： Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound

摘要： 我们通过将Schur-Horn主要化定理应用于密度矩阵的本征值分布和对角线元素，开发了一个严格的框架来量化有限维系统中的量子相干性。 在此基础上，我们引入了一套通用的相干性度量，包括相对交叉熵的相干性和其部分变体，在不可区分操作下满足所有资源理论公理。 这种统一的方法澄清了冯·诺依曼-塔利斯熵空间中物理可实现状态的几何边界，并揭示了退化的相干性浓缩现象，其中本征值谱的对称性使得在高维系统中能够增强相干性的提取。 此外，我们通过细化Maassen-Uffink界限以考虑不同测量基之间的最大本征值，从而加强了基于熵的不确定性关系。 这种细化加深了熵与不确定性之间的联系，为量子信息任务提供了具有操作意义的约束。 总之，我们的研究结果展示了主要化在量子相干性资源理论分析中的强大作用，这为量子信息处理的基础研究和实际应用提供了有价值的工具。 显示英文摘要

摘要： We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this foundation, we introduce a versatile suite of coherence measures, including the relative cross-entropy of coherence and its partial variants, that satisfy all resource theoretic axioms under incoherent operations. This unifying approach clarifies the geometric boundaries of physically realizable states in von Neumann-Tsallis entropy space and uncovers the phenomenon of degenerate coherence distillation where symmetry in the eigenvalue spectrum enables enhanced coherence extraction in higher-dimensional systems. In addition, we strengthen the entropy-based uncertainty relation by refining the Maassen-Uffink bound to account for the largest eigenvalues across distinct measurement bases. This refinement forges a deeper connection between entropy and uncertainty, which yields operationally meaningful constraints for quantum information tasks. Altogether, our findings illustrate the power of majorization in resource-theoretic analyses of quantum coherence, which offer valuable tools for both fundamental research and real-world applications in quantum information processing.