Metrics on completely positive maps via noncommutative geometry

Jonas Eidesen (University of Newcastle)

Thursday 5th November 15:00-16:00
Maths 311B

Abstract

In this talk I will discuss methods of inducing metrics on the set of unital completely positive maps between C*-algebras by employing seminorms arising in noncommutative geometry. The main approach relies on the development of an infinite-dimensional C*-algebraic analogue of the Choi-Jamiolkowski isomorphism. Under suitable conditions, the induced metrics satisfy the quantum information theoretic properties of stability and chaining. Moreover, I will show how to generate such metrics using constructions native to noncommutative geometry, by for example using external Kasparov products of spectral triples. This work is joint with Are Austad, Erik Bédos, Nadia S. Larsen, and Tron Omland.

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