Maximal exponent of the Lorentz cones
We show that the maximal exponent (i.e., the minimum number of iterations required for a primitive map to become strictly positive) of the $n$-dimensional Lorentz cone is equal to $n$. As a byproduct, we show that the optimal exponent in the quantum Wielandt inequality for qubit channels is equal to...
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| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.649/ |
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| author | Aubrun, Guillaume Bai, Jing |
| author_facet | Aubrun, Guillaume Bai, Jing |
| author_sort | Aubrun, Guillaume |
| collection | DOAJ |
| description | We show that the maximal exponent (i.e., the minimum number of iterations required for a primitive map to become strictly positive) of the $n$-dimensional Lorentz cone is equal to $n$. As a byproduct, we show that the optimal exponent in the quantum Wielandt inequality for qubit channels is equal to $3$. |
| format | Article |
| id | doaj-art-90f356423567435a9a78c47efc1aef6c |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-90f356423567435a9a78c47efc1aef6c2025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111379138810.5802/crmath.64910.5802/crmath.649Maximal exponent of the Lorentz conesAubrun, Guillaume0Bai, Jing1Institut Camille Jordan, Université Claude Bernard Lyon 1, CNRS, INRIA, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, FranceInstitut Camille Jordan, Université Claude Bernard Lyon 1, CNRS, INRIA, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France; School of Mathematics, Harbin Institute of Technology, 92 West Dazhi Street, Nangang District, 150001 Harbin, ChinaWe show that the maximal exponent (i.e., the minimum number of iterations required for a primitive map to become strictly positive) of the $n$-dimensional Lorentz cone is equal to $n$. As a byproduct, we show that the optimal exponent in the quantum Wielandt inequality for qubit channels is equal to $3$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.649/Lorentz coneMaximal exponentQuantum Wielandt inequality |
| spellingShingle | Aubrun, Guillaume Bai, Jing Maximal exponent of the Lorentz cones Comptes Rendus. Mathématique Lorentz cone Maximal exponent Quantum Wielandt inequality |
| title | Maximal exponent of the Lorentz cones |
| title_full | Maximal exponent of the Lorentz cones |
| title_fullStr | Maximal exponent of the Lorentz cones |
| title_full_unstemmed | Maximal exponent of the Lorentz cones |
| title_short | Maximal exponent of the Lorentz cones |
| title_sort | maximal exponent of the lorentz cones |
| topic | Lorentz cone Maximal exponent Quantum Wielandt inequality |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.649/ |
| work_keys_str_mv | AT aubrunguillaume maximalexponentofthelorentzcones AT baijing maximalexponentofthelorentzcones |