Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
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| Format: | Preprint |
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2025
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| _version_ | 1866915326527012864 |
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| author | Aziz, Tariq Song, Meng-Long Ye, Liu Wang, Dong |
| author_facet | Aziz, Tariq Song, Meng-Long Ye, Liu Wang, Dong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound Aziz, Tariq Song, Meng-Long Ye, Liu Wang, Dong Quantum Physics 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. |
| title | Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.09110 |