# Entanglement entropy of Bell-network states in LQG: Analytical and numerical results

## TL;DR

This paper develops analytical and numerical methods to evaluate entanglement entropy in Bell-network states within loop quantum gravity, revealing area-law behavior and non-typical entanglement properties.

## Contribution

It introduces algorithms and analytical techniques to compute entanglement entropy in Bell-network states for arbitrary graphs, including bounds and area-law results.

## Key findings

- Bell-network states exhibit non-typical entanglement properties.
- Entanglement entropy obeys an area law in the large-spin regime.
- Developed algorithms for computing Rènyi entropy on arbitrary graphs.

## Abstract

Bell-network states are loop-quantum-gravity states that glue quantum polyhedra with entanglement. We present an algorithm and a code that evaluates the reduced density matrix of a Bell-network state and computes its entanglement entropy. In particular, we use our code for simple graphs to study properties of Bell-network states and to show that they are non-typical in the Hilbert space. Moreover, we investigate analytically Bell-network states on arbitrary finite graphs. We develop methods to compute the R\'enyi entropy of order p for a restriction of the state to an arbitrary region. In the uniform large-spin regime, we determine bounds on the entanglement entropy and show that it obeys an area law. Finally, we discuss the implications of our results for correlations of geometric observables.