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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]
Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 194555604
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Coherence as generalized conditional entropy: α - z -Rényi uncertainty relations.
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  Data: <searchLink fieldCode="AR" term="%22Xue%2C+Ya-Jia%22">Xue, Ya-Jia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xueyajia07@163.com</i><br /><searchLink fieldCode="AR" term="%22Luo%2C+Yu%22">Luo, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> penroseluoyu@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 2026, Vol. 59 Issue 24, p1-16. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Quantum+coherence%22">Quantum coherence</searchLink><br /><searchLink fieldCode="DE" term="%22Renyi's+entropy%22">Renyi's entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+measurement%22">Quantum measurement</searchLink>
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  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1088/1751-8121/ae748b
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      – Code: eng
        Text: English
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      – SubjectFull: Quantum coherence
        Type: general
      – SubjectFull: Renyi's entropy
        Type: general
      – SubjectFull: Quantum measurement
        Type: general
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      – TitleFull: Coherence as generalized conditional entropy: α - z -Rényi uncertainty relations.
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            NameFull: Xue, Ya-Jia
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              M: 06
              Text: 2026
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              Y: 2026
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              Value: 24
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            – TitleFull: Journal of Physics A: Mathematical & Theoretical
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