Year: 2026
Type: preprint
Abstract: We study a multilinear optimization problem for tensors with bounded Frobenius norm, where each of the $k$ local factors of dimension $d$ is chosen from a convex set. We give a deterministic algorithm running in time $d^{O(k)}$ for constant additive approximations. As applications, we obtain the first polynomial-time algorithms at constant accuracy for weak membership in the nuclear-norm unit ball of high-order tensors and for multipartite quantum separability in Frobenius norm. Our approach views tensor optimization as a cooperative multiprover game and combines this perspective with a recursive spectral compression procedure. We then show that related ideas admit a quantum implementation when the input state is given through copies, rather than an explicit classical description. In this setting, we obtain an algorithm to solve Frobenius-norm separability testing using $\text{poly}(k)$ copies and $\text{poly}(k\log d)$ time.
Source: arXiv (Cornell University)
Authors: Bernasconi, Martino, Malavolta, Giulio
Institution: Bocconi University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7220379132