Benjamin McKenna: Moment-based approach to the injective norm of random tensors

mercredi 8 avr. 2026, 14:00 → 15:00 Europe/Paris

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 present a new kind of “moment method” for giving upper bounds on the expected injective norm of real and complex random tensors, corresponding to lower bounds on the geometric entanglement of random quantum states. Relative to prior approaches, the moment method has the benefit of being nonasymptotic, relatively elementary, and applicable to non-Gaussian models, while giving bounds that are sometimes tight. Joint work with Stéphane Dartois.