Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables

TL;DR

This paper develops improved sum uncertainty relations for multiple quantum observables using variance and Wigner-Yanase skew information, providing tighter bounds and demonstrating their advantages through examples.

Contribution

It introduces new, tighter sum uncertainty inequalities for multiple observables based on variance and skew information, advancing quantum uncertainty theory.

Findings

Derived improved uncertainty inequalities for N observables.

Provided examples illustrating the advantages of the new inequalities.

Showed the bounds are tighter than existing relations.

Abstract

We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty relations. Detailed examples are provided to illustrate the advantages of our uncertainty inequalities.