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arXiv · 2503.09110

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

Tariq Aziz·Meng-Long Song·Liu Ye·Dong Wang
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Abstract

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.

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Tariq Aziz, Meng-Long Song, Liu Ye, Dong Wang. 2025-05-28. Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound. https://doi.org/10.1103/physrevresearch.7.023221

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