Tighter sum uncertainty relations via metric-adjusted skew information

TL;DR

This paper introduces new, tighter uncertainty relations for quantum observables and channels using metric-adjusted skew information, improving upon existing bounds and applicable to various skew information measures.

Contribution

The paper develops three general norm inequalities to derive stronger uncertainty relations for finite quantum observables and channels, including special cases like Wigner-Yanase-Dyson skew information.

Findings

New uncertainty relations are tighter than previous bounds.

Two types of lower bounds for channel uncertainty are compared, with a tight lower bound identified.

Examples demonstrate the effectiveness of the new uncertainty relations.

Abstract

In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.