56:55
published on July 18, 2025
Harmonic maps in high-dimensional spheres, representations and random matrices (4/4)
By Antoine Song
Injective norm of real and complex random tensors
Appears in 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.
