Maximal exponent of the Lorentz cones

Guillaume Aubrun (1, 2) , Jing Bai (3)

1 PSPM - Probabilités, statistique, physique mathématique
2 QINFO - Traitement optimal de l'information avec des dispositifs quantiques
3 ICJ - Institut Camille Jordan

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.

Mots clés: Lorentz cone; Maximal exponent; Quantum Wielandt inequality

Domaines: Mathématiques [math]

Guillaume Aubrun, Jing Bai. Maximal exponent of the Lorentz cones. 2023. ⟨hal-04398595⟩