On bounds of Tsallis relative entropy and an inequality for generalized skew information

TL;DR

This paper investigates bounds on Tsallis relative entropy and introduces an inequality for generalized skew information, enhancing the mathematical tools for quantum information theory through trace inequalities.

Contribution

It provides new upper and lower bounds for Tsallis relative entropy and establishes an inequality for generalized skew information using a generalized correlation measure.

Findings

Derived new bounds for Tsallis relative entropy

Compared existing and new bounds for tightness

Proposed an inequality for generalized skew information

Abstract

Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.