Graph restricted tensors: building blocks for holographic networks
Abstract
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this problem by encoding these constraints in a graph is advocated; the resulting objects are called ``graph-restricted tensors''. This framework encompasses several examples previously treated in the literature, such as 1-uniform multipartite states, quantum states related to dual unitary operators and absolutely maximally entangled states (AME) corresponding to 2-unitary matrices. Original examples of presented graph-restricted tensors are motivated by tensor network models for the holographic principle. In concrete cases we find exact analytic solutions, demonstrating thereby that there exists a vast landscape of non-stabilizer tensors useful for the lattice models of holography.
Keywords
Cite
@article{arxiv.2512.23005,
title = {Graph restricted tensors: building blocks for holographic networks},
author = {Rafaĺ Bistroń and Márton Mestyán and Balázs Pozsgay and Karol Życzkowski},
journal= {arXiv preprint arXiv:2512.23005},
year = {2026}
}
Comments
15 pages, v2: minor changes