On the convex characterisation of the set of unital quantum channels

Rodriguez-Ramos, C. ORCID: 0009-0009-0112-4391 and Wilmott, C.M., 2023. On the convex characterisation of the set of unital quantum channels. Journal of Physics A: Mathematical and Theoretical. ISSN 1751-8113

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In this paper, we consider the convex structure of the set of unital quantum channels. To do this, we introduce a novel framework to construct and characterise different families of low-rank unital quantum maps. In this framework, unital quantum maps are represented as a set of complex parameters on which we impose a set of constraints. The different families of unital maps are obtained by mapping those parameters into the operator representation of a quantum map. For these families, we also introduce a scalar measuring their distance to the set of mixed-unitary maps. We consider the particular case of qutrit channels which is the smallest set of maps for which the existence of non-unitary extremal maps is known. In this setting, we show how our framework generalises the description of well-known maps such as the antisymmetric Werner-Holevo map but also novel families of qutrit maps.

Item Type: Journal article
Publication Title: Journal of Physics A: Mathematical and Theoretical
Creators: Rodriguez-Ramos, C. and Wilmott, C.M.
Publisher: IOP Publishing
Date: 27 September 2023
ISSN: 1751-8113
Rights: © 2023 The Author(s). Published by IOP Publishing Ltd. As the Version of Record of this article is going to be / has been published on a gold open access basis under a CC BY 4.0 licence, this Accepted Manuscript is available for reuse under a CC BY 4.0 licence immediately. Everyone is permitted to use all or part of the original content in this article, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by/4.0
Divisions: Schools > School of Science and Technology
Record created by: Laura Ward
Date Added: 18 Oct 2023 07:48
Last Modified: 18 Oct 2023 07:48
URI: https://irep.ntu.ac.uk/id/eprint/49998

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