During this lecture I will introduce a framework to quantify the ``Lipschitz'' cost of quantum channels on von Neumann algebras. Our approach of using Lipschitz seminorms is inspired by quantum optimal transport theory. After discussing some of the fundamental properties which our cost measure satisfies, I will discuss how we can derive effective lower bounds for gate complexities and simulation costs of both Hamiltonian simulations and open system dynamics
Back to Workshop II: Dynamics of Density Operators