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A Survey of Recent Inequalities for Relative Operator Entropy

In: Operations Research, Engineering, and Cyber Security

Author

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  • Silvestru Sever Dragomir

    (Victoria University
    University of Witwatersrand)

Abstract

The concepts of relative operator entropy and operator entropy play an important role in different subjects, such as statistical mechanics, information theory, dynamical systems and ergodic theory, biology, economics, human and social sciences. They are closely related to the problem of the quantification of entanglement, the distinguishability of quantum states and to thermodynamical ideas. In this paper we survey some recent inequalities obtained by the author for the relative operator entropy S ⋅ | ⋅ , $$S\left (\cdot \vert \cdot \right ),$$ for positive invertible operators A and B in general, and, in particular when they satisfy the boundedness condition mA ≤ B ≤ MA for some m, M with 0

Suggested Citation

  • Silvestru Sever Dragomir, 2017. "A Survey of Recent Inequalities for Relative Operator Entropy," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Operations Research, Engineering, and Cyber Security, pages 199-229, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-51500-7_10
    DOI: 10.1007/978-3-319-51500-7_10
    as

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