Injective norm of real and complex random tensors

Apparaît dans la collection : 2024 - PC2 - Random tensors and related topics

The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipartite entanglement of quantum states, where it is known as the geometric entanglement. We give a high-probability upper bound on the injective norm of real and complex Gaussian random tensors, corresponding to a lower bound on the geometric entanglement of random quantum states. The proof is based on spin-glass methods, the Kac—Rice formula, and recent progress coming from random matrices. Joint work with Stéphane Dartois.

Informations sur la vidéo

Date de captation 18/10/2024
Date de publication 08/11/2024
Institut IHP
Licence CC BY-NC-ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Alexandre Duplessis
Format MP4
Lieu IHP - Hermite Amphitheater

Données de citation

DOI 10.57987/IHP.2024.PC2.016
Citer cette vidéo McKenna, Benjamin (18/10/2024). Injective norm of real and complex random tensors. IHP. Audiovisual resource. DOI: 10.57987/IHP.2024.PC2.016
URL https://dx.doi.org/10.57987/IHP.2024.PC2.016

Domaine(s)

Probabilités

Bibliographie

"Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement." Stephane Dartois and Benjamin McKenna, 2024. arXiv:2404.03627v1