Analysis Seminar

Andre Kornell, UC Davis

"Quantum Extensions of Ordinary Maps"

Noncommutative mathematics views unital C*-algebras to be a quantum generalization of compact Hausdorff spaces. In this context, unital C*-algebras may be termed quantum compact Hausdorff spaces. Recent research in quantum information theory has stimulated interest in families of maps indexed by such a quantum compact Hausdorff space. Some map extension problems that are unsolvable in the classical setting become solvable in the quantum setting. In other words, some maps admit no family of extensions indexed by an ordinary nonempty compact Hausdorff space, but do admit a family of extensions indexed by a quantum nonempty compact Hausdorff space. Does the same phenomenon occur for finite T_0 spaces? An affirmative answer would produce new examples of quantum pseudotelepathy.

MC 5417