Abstract: Let C be a compact convex set (in a locally convex topological vector space). By Choquet’s theorem, every point in C is the barycenter of a probability measure supported on the extreme points. When this representing measure is unique, C is called a simplex. Simplices arise naturally in various fields of mathematics: the space […]
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 […]
Abstract: An isometry between two normed vector spaces is a linear map that preserves the norm (i.e., the length of each output agrees with the length of its input). For […]
