Graph restricted tensors: building blocks for holographic networks

TL;DR

This paper introduces graph-restricted tensors as a new framework to analyze highly entangled quantum states, with applications to holographic tensor network models and exact solutions demonstrating their potential in holography.

Contribution

The paper develops a novel graph-based framework for constructing and analyzing highly entangled quantum states, including new examples relevant to holographic tensor networks.

Findings

Exact analytic solutions for specific graph-restricted tensors.

Existence of a vast landscape of non-stabilizer tensors for holography.

Unified framework encompassing known classes like AME and dual unitary states.

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.