2024/04/04 by Stéphane Dartois, Dartois, Stephane, Benjamin McKenna +1 · 5 citations
Computer Science · Mathematics · #15B52 #60B20 #81P42 #81P45 #82D30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2404.03627
openalex publication_date 2024/04/04 · openalex created_date 2024/04/06 · openalex updated_date 2026/08/01
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. In this paper, 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, and to a bound on the ground-state energy of a particular multispecies spherical spin glass model. For some cases of our model, previous work used ε-net techniques to identify the correct order of magnitude; in the present work, we use the Kac--Rice formula to give a one-sided bound on the constant which we believe to be tight.