Korean J. Math.  Vol 26, No 3 (2018)  pp.349-371
DOI: https://doi.org/10.11568/kjm.2018.26.3.349

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

Silvestru Sever Dragomir

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.


Keywords


Selfadjoint bounded linear operators, Functions of matrices, Trace of matrices, Quantum divergence measures, Umegaki and Tsallis relative entropies.

Subject classification

47A63, 47A99.

Sponsor(s)



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References


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