Analysis Seminar: Metrics on quantum channels from noncommutative geometry (Tron Omland, University of Oslo and Norwegian National Security Authority)

Abstract: We study metrics on completely positive maps, and in particular on quantum channels, induced by seminorms from noncommutative geometry. Using an infinite-dimensional analogue of the Choi–Jamiołkowski correspondence, we construct such metrics and show that, under suitable assumptions, they satisfy stability and chaining. I will present the main ideas and explain how spectral triples and related constructions give rise to distances between quantum processes. This is joint work with Austad, Bedos, Eidesen, and Larsen.