Building Holographic Entanglement by Measurement

TL;DR

This paper introduces a method to create quantum states with holographic entanglement properties by discretizing a bulk geometry into a graph, evolving it with interactions, and measuring bulk nodes, reproducing the Ryu-Takayanagi formula.

Contribution

The authors propose a novel framework for engineering holographic entanglement structures using graph-based discretization and measurements, applicable to various geometries.

Findings

Numerical results show approximate agreement with the Ryu-Takayanagi formula.

The approach is general and applicable to hyperbolic and wormhole geometries.

Implementation requires only Gaussian operations and measurements, suitable for photonic and cold-atom systems.

Abstract

We propose a framework for preparing quantum states with a holographic entanglement structure, in the sense that the entanglement entropies are governed by minimal surfaces in a chosen bulk geometry. We refer to such entropies as holographic because they obey a relation between entropies and bulk minimal surfaces, known as the Ryu-Takayanagi formula, that is a key feature of holographic models of quantum gravity. Typically in such models, the bulk geometry is determined by solving Einstein's equations. Here, we simply choose a bulk geometry, then discretize the geometry into a coupling graph comprising bulk and boundary nodes. Evolving under this graph of interactions and measuring the bulk nodes leaves behind the desired pure state on the boundary. We numerically demonstrate that the resulting entanglement properties approximately reproduce the predictions of the Ryu-Takayanagi formula in the chosen bulk geometry. We consider graphs associated with hyperbolic disk and wormhole geometries, but the approach is general. The minimal ingredients in our proposal involve only Gaussian operations and measurements and are readily implementable in photonic and cold-atom platforms.