Schr\"odinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure

TL;DR

This paper develops generalized Schr"odinger-type uncertainty relations using Wigner-Yanase-Dyson skew information, extended correlation measures, and metric adjusted correlation measures, broadening the theoretical framework of quantum uncertainty.

Contribution

It introduces new generalized uncertainty relations based on advanced correlation measures, extending previous results in quantum information theory.

Findings

Generalized Schr"odinger-type uncertainty relation using Wigner-Yanase-Dyson skew information.

Uncertainty relation derived from a two-parameter extended correlation measure.

Further generalization employing metric adjusted correlation measure.

Abstract

In this paper, we give a Schr\"odinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schr\"odinger-type uncertainty relation by use of a two-parameter extended correlation measure. Moreover, we give the further generalization for Schr\"odinger-type uncertainty relation by metric adjusted correlation measure. These results generalize our previous result in [Phys. Rev. A, Vol.82(2010), 034101].