Uncertainty Relation for the Wigner-Yanase Skew Information and Quantum Sobolev Inequalities

TL;DR

This paper investigates uncertainty inequalities related to the Wigner-Yanase skew information and their links to quantum Sobolev inequalities, providing new mathematical insights into quantum information theory.

Contribution

It introduces new uncertainty inequalities for quantum Fisher information measures and connects them to quantum Sobolev inequalities, expanding theoretical understanding.

Findings

Derived new inequalities for commutators

Connected quantum Fisher information to Sobolev inequalities

Proposed open problems for further research

Abstract

This note explores uncertainty inequalities for quantum analogues of the Fisher information including the Wigner-Yanase skew information, and their connection to the quantum Sobolev inequalities proved by the author in [Journal of Functional Analysis, 286 (10) 2024]. Some additional inequalities concerning commutators are derived and others are left as open problems.