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

• URL: http://arxiv.org/abs/2503.09110v4
• Date: Wed, 28 May 2025 12:35:47 GMT
• Title: Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• Authors: Tariq Aziz, Meng-Long Song, Liu Ye, Dong Wang,
• Abstract summary: We introduce a versatile suite of coherence measures that satisfy all resource theoretic axioms under incoherent operations.<n>This unifying approach clarifies the geometric boundaries of physically realizable states in von Neumann-Tsallis entropy space.<n>We strengthen the entropy-based uncertainty relation by refining the Maassen-Uffink bound to account for the largest eigenvalues across distinct measurement bases.
• Score: 4.138060581023728
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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