Title: Metrics on completely positive maps via noncommutative geometry
Abstract: We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an infinite-dimensional C*-algebraic analogue of the Choi–Jamiołkowski isomorphism. Under suitable conditions, we show that the induced metrics satisfy the quantum information theoretic properties of stability and chaining. Moreover, we show how to generate such metrics using constructions native to noncommutative geometry, by for example using external Kasparov products of spectral triples. In this talk I will present the main results in this paper as well as the main technical tools we needed to develop. This is joint work with Are Austad, Erik Bédos, Nadia S. Larsen, and Tron Omland.