Recorded 28 April 2025. Roy Araiza of the University of Illinois at Urbana-Champaign presents "Lipschitz Cost of Quantum Channels on von Neumann Algebras" at IPAM's Dynamics of Density Operators Workshop. Abstract: 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 Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-dynamics-of-density-operators/