본문 바로가기
KERD
논문KCI 등재

Inequalities for quantum $f$-divergence of convex functions and matrices

Silvestru Sever Dragomir
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2018.09|한국수학논문집 (Korean Journal of Mathematics)|제26권 제3호|pp. 349-371

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Selfadjoint bounded linear operatorsFunctions of matricesTrace of matricesQuantum divergence measuresUmegaki and Tsallis relative entropies.
주제분류수학

초록

Some inequalities for quantum $f$-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum $f$-divergence in terms of variational and $\chi ^{2}$-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

Abstract

Some inequalities for quantum $f$-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum $f$-divergence in terms of variational and $\chi ^{2}$-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

참고문헌 (26)

  1. P. Cerone, "Approximation of the integral mean divergence and f-divergence via mean results", Math. Comput. Modelling, 42(1-2), pp.207~219 (2005)[DOI]
  2. P. Cerone, "Bounds on extended f-divergences for a variety of classes", Kybernetika (Prague), 40(6), pp.745~756 (2004)
  3. I. Csiszar, "Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten", (German) Magyar Tud. Akad. Mat. Kutato Int. Kozl., 8, pp.85~108 (1963)
  4. S. S. Dragomir, "Bounds for the normalized Jensen functional", Bull. Austral. Math. Soc., 74(3), pp.471~476 (2006)[DOI]
  5. S. S. Dragomir, "Some inequalities for (m, M)-convex mappings and applications for the Csiszar <TEX>$\Phi$<", TEX>-divergence in information theory, 2001, pp.33, 35~50
  6. S. S. Dragomir, "Some inequalities for two Csiszar divergences and applications", Mat. Bilten., 25, pp.73~90 (2001)
  7. S. S. Dragomir, "An upper bound for the Csiszar f-divergence in terms of the variational distance and applications", Panamer. Math. J., 12(4), pp.43~54 (2002)
  8. S. S. Dragomir, "Upper and lower bounds for Csiszar f-divergence in terms of Hellinger discrimination and applications", Nonlinear Anal. Forum, 7(1), pp.1~13 (2002)
  9. S. S. Dragomir, "Bounds for f-divergences under likelihood ratio constraints", Appl. Math., 48(3), pp.205~223 (2003)[DOI]
  10. S. S. Dragomir, "New inequalities for Csiszar divergence and applications", Acta Math. Vietnam., 28(2), pp.123~134 (2003)
  11. S. S. Dragomir, "A generalized f-divergence for probability vectors and applications", Panamer. Math. J., 13(4), pp.61~69 (2003)
  12. S. S. Dragomir, "Some inequalities for the Csiszar <TEX>$\varphi$<", TEX>-divergence when <TEX>$\varphi$<, Ital. J. Pure Appl. Math., pp.2004, 15[DOI]
  13. S. S. Dragomir, "A converse inequality for the Csiszar <TEX>$\Phi$<", TEX>-divergence, 2004, pp.20(1), 35~53
  14. S. S. Dragomir, "Some general divergence measures for probability distributions", Acta Math. Hungar., 109(4), pp.331~345 (2005)[DOI]
  15. S. S. Dragomir, "A refinement of Jensen's inequality with applications for f-divergence measures", Taiwanese J. Math., 14(1), pp.153~164 (2010)[DOI]
  16. S. S. Dragomir, "A generalization of f-divergence measure to convex functions defined on linear spaces", Commun. Math. Anal., 15(2), pp.1~14 (2013)
  17. F. Hiai, "From quasi-entropy to various quantum information quantities", Publ. Res. Inst. Math. Sci., 48(3), pp.525~542 (2012)[DOI]
  18. F. Hiai, "Quantum f-divergences and error correction", Rev. Math. Phys., 23(7), pp.691~747 (2011)[DOI]
  19. P. Kafka, "On powers of f-divergence defining a distance", Studia Sci. Math. Hungar., 26, pp.415~422 (1991)
  20. F. Liese, "Convex Statistical Distances, Band 95" (1987), Teubuer - Texte zur Mathematik
  21. F. Osterreicher, "A new class of metric divergences on probability spaces and its applicability in statistics", Ann. Inst. Statist. Math., 55(3), pp.639~653 (2003)[DOI]
  22. D. Petz, "Quasi-entropies for states of a von Neumann algebra", Publ. RIMS. Kyoto Univ., 21, pp.781~800 (1985)
  23. D. Petz, "Quasi-entropies for finite quantum systems", Rep. Math. Phys., 23, pp.57~65 (1986)[DOI]
  24. D. Petz, "From quasi-entropy", Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 55, pp.81~92 (2012)
  25. D. Petz, "From f-divergence to quantum quasi-entropies and their use", Entropy, 12(3), pp.304~325 (2010)[DOI]
  26. M. B. Ruskai, "Inequalities for traces on von Neumann algebras", Commun. Math. Phys., 26, pp.280~289 (1972)[DOI]

관련 논문AI추천

On Estimates for Fractional Tsallis Relative Operator EntropyAzizollah Babakhani, Behare Hosseini, Ismail Nikoufar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제4호Inequalities of operator valued quantum skew information이미라, 최병진대한수학회 · 대한수학회보2021 · 제58권 제1호Some trace inequalities for convex functions of selfadjoint operators in Hilbert spacesSilvestru Sever Dragomir강원경기수학회 · 한국수학논문집2016 · 제24권 제2호On numerical range and numerical radius of convex function operatorsAbdelouahab Mansour, Khaoula Zaiz강원경기수학회 · 한국수학논문집2019 · 제27권 제4호Improvement of Jensen's Inequality in terms of G^ateaux Derivatives for Convex Functions in Linear Spaces with ApplicationsJosip Pecaric, Muhammad Adil Khan, Sadia Khalid경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제4호SOME INEQUALITIES FOR THE WEIGHTED CHAOTICALLY GEOMETRIC MEANSilvestru Sever Dragomir한국수학교육학회 · 이론수학과 교직수학2019 · 제26권 제3호

이 간행물의 다른 논문 (11건)

Fuzzy homomorphism theorems on groupsGezahagne Mulat Addispp. 373-385Shifting and modulation for the convolution product of functionals in a generalized Fresnel class김병수, 박연희pp. 387-403Growth analysis of composite entire functions from the view point of relative $(p,q)$-th orderTanmay Biswaspp. 405-424Surfaces generated via the evolution of spherical image of a space curveTaha Youssef Shaker, R. A. Hussien, M. A. Soliman, Nassar H.Abdel-Allpp. 425-437Derived crossed modulesTunçar Şahanpp. 439-458
원문 보기