Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems

arXiv:2611.04263v1 Announce Type: new Abstract: Building on our earlier results for closed quantum systems, we investigate the dynamical evolution of quantum fluctuations and their connections to Fisher information and the quantum operations describing open-system dynamics. Starting from a general expression for the time derivative of an observable's uncertainty, we derive an alternative upper bound on fluctuation growth in an open quantum system using the Cauchy-Schwarz inequality. The resulting bound separates contributions from the evolution of the quantum state and the explicit time dependence of the observable, reducing to a known result for closed-system dynamics.