SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 20: Concepts and Methods II

QI 20.4: Talk

Wednesday, March 8, 2023, 15:15–15:30, B302

Continuity of robustness measures in quantum resource theories — Jonathan Schluck, Gláucia Murta, Hermann Kampermann, Dagmar Bruß, and •Nikolai Wyderka — Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany

Robustness measures provide an intuitive and operational way to quantify resources in quantum resource theories, such as entanglement and coherence. Despite exhibiting useful mathematical properties like monotonicity, the use of robustness measures is hindered by the fact that some of their properties like continuity remain unclear, in particular when the set of resource-free states is non-convex. To that end, we investigate continuity properties of different robustness measures by showing that their continuity depends on the shape of the set of free states. In particular, we show that in many cases star-convexity is sufficient for Lipschitz-continuity, and we provide specific examples of sets leading to non-continuous robustness measures. Finally, we illustrate the applicability of our results by introducing the robustness of teleportation fidelity and by deriving bounds on the robustness of quantum discord.