Tighter uncertainty relations based on $(\alpha,\beta,\gamma)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

TL;DR

This paper introduces a new form of skew information for quantum channels, deriving tighter sum uncertainty relations using operator norm inequalities, applicable to various types of channels and special cases.

Contribution

It proposes a novel ($oldsymbol{ ext{α,β,γ}}$) modified weighted Wigner-Yanase-Dyson skew information and derives tighter uncertainty relations for quantum channels.

Findings

Derived tighter sum uncertainty relations for quantum channels.

Demonstrated the effectiveness of the new inequalities with detailed examples.

Applicable to various forms of skew information and special cases.

Abstract

We use a novel formation to illustrate the ($\alpha,\beta,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary $N$ quantum channels and for unitary channels. These uncertainty inequalities are shown to be tighter than the existing ones by a detailed example. Our results are also applicable to the modified weighted Wigner-Yanase-Dyson (MWWYD) skew information and the ($\alpha,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\gamma$) MWWYD) skew information of quantum channels as special cases.