A note on uncertainty relations of metric-adjusted skew information

TL;DR

This paper develops tighter uncertainty relations based on metric-adjusted skew information for quantum observables, channels, and unitaries, generalizing previous results and illustrating advantages with examples.

Contribution

It introduces improved uncertainty relations using metric-adjusted skew information, extending the framework to quantum channels and unitaries, and generalizing existing relations.

Findings

Derived tighter uncertainty relations for quantum observables.

Extended the framework to quantum channels and unitaries.

Provided examples demonstrating the advantages of the new relations.

Abstract

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova-Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods.