The quantum geometry of electronic states has recently emerged as a unifying conceptual framework for understanding phenomena such as localization in insulators, interactions in flatband systems, and sum rules for linear response functions. In this talk, we will show how for generic systems at arbitrary temperatures, there is a deep connection between quantum geometric data and quantum information. Using time-dependent perturbation theory, we will derive a time-dependent generalization of the information-theoretic Bures metric related to the linear response functions, unifying previous results for the quantum metric in various limits. We will show this allows for experimental measurements of quantum geometry in scattering experiments, allowing us to compare the quantum geometry in ionic and covalent insulators. Finally, we will explore how this viewpoint lets us define geometric quantities beyond the quantum metric related to nonlinear response functions.