Trace inequalities on a generalized Wigner-Yanase skew information

TL;DR

This paper introduces a generalized Wigner-Yanase skew information and establishes new trace inequalities related to quantum uncertainty, extending previous uncertainty relations and providing broader mathematical tools for quantum information theory.

Contribution

The paper presents a novel generalized Wigner-Yanase skew information and derives new trace inequalities, expanding the mathematical framework for quantum uncertainty analysis.

Findings

Derived a generalized Wigner-Yanase skew information.

Established new trace inequalities related to quantum uncertainty.

Extended Luo's uncertainty relation to a broader context.

Abstract

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixure. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued.