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Coherence as generalized conditional entropy: α - z -Rényi uncertainty relations.

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Title: Coherence as generalized conditional entropy: α - z -Rényi uncertainty relations.
Authors: Xue, Ya-Jia1 (AUTHOR) xueyajia07@163.com, Luo, Yu1 (AUTHOR) penroseluoyu@gmail.com
Source: Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 24, p1-16. 16p.
Subjects: Quantum coherence, Renyi's entropy, Quantum measurement
Abstract: We establish a rigorous equivalence between quantum coherence measures defined by the sandwiched Rényi relative entropy and generalized conditional entropies associated with auxiliary quantum systems, providing a direct operational interpretation of sandwiched Rényi relative entropy of coherence as the conditional uncertainty of projective measurement outcomes with quantum memory. Motivated by this connection, we develop a coherence-based approach to quantum uncertainty relations. Within this approach, we introduce a coherence measure induced by the two-parameter α - z -Rényi relative entropy and derive corresponding uncertainty relations for both pure and mixed quantum states. The resulting state-independent bounds recover known results in appropriate limits and yield tighter bounds over a broad parameter regime. Our results provide a systematic connection between quantum coherence, generalized conditional entropies, and uncertainty relations, thereby offering a unified perspective on quantum uncertainty in terms of Rényi-type information measures. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We establish a rigorous equivalence between quantum coherence measures defined by the sandwiched Rényi relative entropy and generalized conditional entropies associated with auxiliary quantum systems, providing a direct operational interpretation of sandwiched Rényi relative entropy of coherence as the conditional uncertainty of projective measurement outcomes with quantum memory. Motivated by this connection, we develop a coherence-based approach to quantum uncertainty relations. Within this approach, we introduce a coherence measure induced by the two-parameter α - z -Rényi relative entropy and derive corresponding uncertainty relations for both pure and mixed quantum states. The resulting state-independent bounds recover known results in appropriate limits and yield tighter bounds over a broad parameter regime. Our results provide a systematic connection between quantum coherence, generalized conditional entropies, and uncertainty relations, thereby offering a unified perspective on quantum uncertainty in terms of Rényi-type information measures. [ABSTRACT FROM AUTHOR]
ISSN:17518113
DOI:10.1088/1751-8121/ae748b