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arXiv · 2512.10842

Metrics on completely positive maps via noncommutative geometry

Are Austad·Erik Bédos·Jonas Eidesen·Nadia S. Larsen·Tron Omland
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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-Jamio\l{}kowski 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.

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Are Austad, Erik Bédos, Jonas Eidesen, Nadia S. Larsen, Tron Omland. 2025-12-11. Metrics on completely positive maps via noncommutative geometry. https://arxiv.org/abs/2512.10842

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