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Open Quantum Systems Decoherence
Metrics on completely positive maps via noncommutative geometry
arXiv
Authors: Are Austad, Erik Bédos, Jonas Eidesen, Nadia S. Larsen, Tron Omland
Year
2025
Paper ID
36689
Status
Preprint
Abstract Read
~2 min
Abstract Words
79
Citations
N/A
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.
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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry.
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