Estimation of Quantum Umlaut Information

arXiv:2610.41282v1 Announce Type: new Abstract: Quantifying correlations is important for understanding how quantum states and channels support information processing. Quantum umlaut information $U$ connects such correlations to reliability in hypothesis testing and certain communication settings, but its known formulas require classical descriptions of the underlying states. To estimate correlations without these descriptions, we introduce measured quantum umlaut information $U^M$ by replacing Umegaki relative entropy with measured relative entropy. Its variational formulation leads to a quantum generative adversarial framework for estimating $U^M$ from measurement statistics of unknown bipartite states and classical-quantum channels.