Entanglement Negativity on Random Spin Networks

TL;DR

This paper studies quantum entanglement in 3D quantum geometry using random spin networks, revealing holographic properties of negativity and effects of bulk entanglement on boundary correlations.

Contribution

It introduces a method to compute typical Rènyi negativity in random spin networks, linking quantum gravity states to classical Ising models and analyzing holographic entanglement features.

Findings

Log negativity exhibits holographic scaling in local entanglement cases.

Bulk entanglement increases negativity and perturbs holographic scaling.

Random spin networks can model quantum geometric entanglement with classical analogs.

Abstract

We investigate multipartite entanglement for quantum states of 3d space geometry, described via generalised random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on entanglement negativity as a well defined witness of quantum correlations for mixed states, in our setting describing generic subregions of the boundary of a quantum 3d region of space. In particular, we consider a generic tripartition of the boundary of an open spin network state and we compute the typical R\'enyi negativity of two boundary subregions A and B immersed in the environment C, explicitly for a set of simple open random spin network states. We use the random character of the spin network to exploit replica and random average techniques to derive the typical R\'enyi negativty via a classical generalised Ising model correspondence, generally used for random tensor networks in the large bond regime. For trivially correlated random spin network states, with only local entanglement between spins located on the network edges, we find that typical log negativity displays a holographic character, in agreement with the results for random tensor networks, in large spin limit. When non-local bulk entanglement between intertwiners at the vertices is considered the negativity increases, while at the same time the holographic scaling is generally perturbed by the bulk contribution.