Abstract
In this paper we introduce the concept of quadratic quantum $f$-divergence measure for a continuos function $f$ defined on the positive semi-axis of real numbers, the invertible matrix $T$ and matrix $V$ by $$\mathcal{S}_{f}\left( V,T\right) :=\mathrm{tr}\left[ \left\vert T^{\ast }\right\vert ^{2}f\left( \left\vert VT^{-1}\right\vert ^{2}\right) \right].$$ Some fundamental inequalities for this quantum $f$-divergence in the case of convex functions are established. Applications for particular quantum divergence measures of interest are also provided.
Acknowledgment
The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the paper.
Citation
Silvestru Sever Dragomir. "The Quadratic Quantum $f$-Divergence of Convex Functions and Matrices." Nihonkai Math. J. 29 (1) 1 - 19, 2018.
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