Inequalities for Quantum f-Divergence of Trace Class Operators in Hilbert Spaces

TL;DR

This paper establishes new inequalities for quantum f-divergence of trace class operators, providing bounds and applications to various divergence measures in quantum information theory.

Contribution

It introduces novel inequalities for quantum f-divergence, including bounds related to variational and chi-distance, with applications to Umegaki and Tsallis entropies.

Findings

Quantum f-divergence is nonnegative for normalized convex functions.

Upper bounds for quantum f-divergence are derived in terms of variational and chi-distance.

Applications to Umegaki and Tsallis relative entropies are demonstrated.

Abstract

Some inequalities for quantum f-divergence of trace class operators in Hilbert spaces 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-distance are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.