## Nihonkai Mathematical Journal

### The Quadratic Quantum $f$-Divergence of Convex Functions and Matrices

Silvestru Sever Dragomir

#### 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.

#### Note

The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the paper.

#### Article information

Source
Nihonkai Math. J., Volume 29, Number 1 (2018), 1-19.

Dates
Revised: 15 February 2018
First available in Project Euclid: 6 February 2019

https://projecteuclid.org/euclid.nihmj/1549422080

Mathematical Reviews number (MathSciNet)
MR3908815

Zentralblatt MATH identifier
07063837

#### Citation

Dragomir, Silvestru Sever. The Quadratic Quantum $f$-Divergence of Convex Functions and Matrices. Nihonkai Math. J. 29 (2018), no. 1, 1--19. https://projecteuclid.org/euclid.nihmj/1549422080

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