Sum uncertainty relations based on $(\alpha,\beta,\gamma)$ weighted Wigner-Yanase-Dyson skew information

TL;DR

This paper introduces new weighted skew information measures and derives improved sum uncertainty relations for multiple observables and quantum channels, advancing quantum uncertainty theory.

Contribution

It proposes the ($oldsymbol{ extalpha,eta,\gamma}$) weighted and modified weighted Wigner-Yanase-Dyson skew information, extending and enhancing existing uncertainty relations.

Findings

Derived a series of new uncertainty inequalities.

Showed that results generalize and improve previous bounds.

Established uncertainty relations for quantum channels.

Abstract

We introduce ($\alpha,\beta,\gamma$) weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) WWYD) skew information and ($\alpha,\beta,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary $N$ mutually noncommutative observables based on ($\alpha,\beta,\gamma$) WWYD skew information. A series of uncertainty inequalities are derived. We show by detailed example that our results cover and improve the previous ones based on the original Wigner-Yanase (WY) skew information. Finally, we establish new sum uncertainty relations in terms of the ($\alpha,\beta,\gamma$) MWWYD skew information for arbitrary $N$ quantum channels.