On the convex characterisation of the set of unital quantum channels

Rodriguez-Ramos, C ORCID: https://orcid.org/0009-0009-0112-4391 and Wilmott, CM, 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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Abstract

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
Identifiers:	Number Type 10.1088/1751-8121/acfddb DOI 1821419 Other
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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