Sum uncertainty relations based on Wigner-Yanase skew information

TL;DR

This paper develops new sum uncertainty relations for multiple quantum observables using Wigner-Yanase skew information, providing insights into noncommutative quantum measurements and comparing with existing inequalities.

Contribution

It introduces novel sum uncertainty inequalities based on skew information for multiple observables, expanding the understanding of quantum uncertainty.

Findings

Derived nontrivial uncertainty inequalities for noncommuting observables

Compared new inequalities with existing ones to analyze their relations

Provided detailed examples illustrating the inequalities

Abstract

We study sum uncertainty relations for arbitrary finite $N$ quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.