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