no. G11
Article de recherche - Analyse fonctionnelle, Géométrie et Topologie
Maximal exponent of the Lorentz cones
[Exposant maximal des cônes de Lorentz]
Aubrun, Guillaume1  ; Bai, Jing2, 1
1Institut Camille Jordan, Université Claude Bernard Lyon 1, CNRS, INRIA, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
2School of Mathematics, Harbin Institute of Technology, 92 West Dazhi Street, Nangang District, 150001 Harbin, China
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1379-1388

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.

Nous démontrons que l’exposant maximal (c’est-à-dire le nombre minimal d’itérations requises pour qu’une application primitive devienne strictement positive) du cône de Lorentz de dimension n est égal à n. Nous montrons également que l’exposant optimal dans l’inégalité de Wielandt quantique pour des canaux agissant sur un qubit est égal à 3.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.649
Classification : 52A20, 51M04
Keywords: Lorentz cone, Maximal exponent, Quantum Wielandt inequality
Mots-clés : Cône de Lorentz, exposant maximal, inégalité de Wielandt quantique

Aubrun, Guillaume  1   ; Bai, Jing  2 , 1

1 Institut Camille Jordan, Université Claude Bernard Lyon 1, CNRS, INRIA, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
2 School of Mathematics, Harbin Institute of Technology, 92 West Dazhi Street, Nangang District, 150001 Harbin, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Maximal exponent of the {Lorentz} cones},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1379--1388},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
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Aubrun, Guillaume; Bai, Jing. Maximal exponent of the Lorentz cones. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1379-1388. doi: 10.5802/crmath.649

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