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Quantum wasserstein distance of order 1 between channels
Dissertation (MSc (Physics))--University of Pretoria, 2023.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613631433146368 |
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| access_status_str | Open Access |
| author2 | Duvenhage, Rocco |
| author_browse | Duvenhage, Rocco |
| author_facet | Duvenhage, Rocco |
| collection | Thesis |
| dc_rights_str_mv | © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Physics))--University of Pretoria, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/94087 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:12.888Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/94087 Quantum wasserstein distance of order 1 between channels Duvenhage, Rocco mapayawitnesss@gmail.com Mapaya, Mathumo UCTD Quantum optimal transport Quantum Wasserstein distance of order 1 Quantum channels Quantum states Composite systems Sustainable Development Goals (SDGs) SDG-04: Quality education Natural and agricultural sciences theses SDG-04 SDG-09: Industry, innovation and infrastructure Natural and agricultural sciences theses SDG-09 Dissertation (MSc (Physics))--University of Pretoria, 2023. We analyse a formulation of the quantum Wasserstein distance of order $1$ and set up a general theory leading to a Wasserstein distance of order $1$ between the unital maps from one specific algebra to another specified algebra. This gives us a metric on the set of unital maps from one composite system to another, which is deeply connected to the reductions of the unital maps. We use the fact that channels are unital maps with extra structure, to systematically define a quantum Wasserstein distance of order $1$ between channels, i.e., a metric on the set of channels. Lastly, the additivity and stability properties of this metric are studied. The National Research Foundation (NRF) and The National Institute for Theoretical and Computational Sciences (NITheCS). Physics MSc (Physics) Unrestricted Faculty of Natural and Agricultural Sciences 2024-01-24T13:57:39Z 2024-01-24T13:57:39Z 2024-04 2023-10-26 Dissertation * A2024 http://hdl.handle.net/2263/94087 Disclaimer letter en © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Quantum optimal transport Quantum Wasserstein distance of order 1 Quantum channels Quantum states Composite systems Sustainable Development Goals (SDGs) SDG-04: Quality education Natural and agricultural sciences theses SDG-04 SDG-09: Industry, innovation and infrastructure Natural and agricultural sciences theses SDG-09 Quantum wasserstein distance of order 1 between channels |
| title | Quantum wasserstein distance of order 1 between channels |
| title_full | Quantum wasserstein distance of order 1 between channels |
| title_fullStr | Quantum wasserstein distance of order 1 between channels |
| title_full_unstemmed | Quantum wasserstein distance of order 1 between channels |
| title_short | Quantum wasserstein distance of order 1 between channels |
| title_sort | quantum wasserstein distance of order 1 between channels |
| topic | UCTD Quantum optimal transport Quantum Wasserstein distance of order 1 Quantum channels Quantum states Composite systems Sustainable Development Goals (SDGs) SDG-04: Quality education Natural and agricultural sciences theses SDG-04 SDG-09: Industry, innovation and infrastructure Natural and agricultural sciences theses SDG-09 |
| url | http://hdl.handle.net/2263/94087 |