Uncertainty Relation for the Wigner-Yanase Skew Information and Quantum Sobolev Inequalities
arXiv:2508.15554
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.
8 pages. Submitted to the book of extended abstract of the book series "Research Perspectives Ghent Analysis and PDE Center", part of the Springer/Birkhäuser Trends in Mathematics series