Gluing polyhedra with entanglement in loop quantum gravity

TL;DR

This paper demonstrates how entanglement in loop quantum gravity enforces the gluing of neighboring quantum polyhedra, revealing the role of entanglement in constructing quantum geometries.

Contribution

It introduces Bell-network states, a new class of entangled states, and analyzes their role in forming glued quantum geometries in loop quantum gravity.

Findings

Entanglement enforces gluing conditions between quantum polyhedra.

Bell-network states naturally produce vector geometries.

Connections to Regge geometries are discussed.

Abstract

In a spin-network basis state, nodes of the graph describe un-entangled quantum regions of space, quantum polyhedra. In this paper we show how entanglement between intertwiner degrees of freedom enforces gluing conditions for neighboring quantum polyhedra. In particular we introduce Bell-network states, entangled states defined via squeezed vacuum techniques. We study correlations of quantum polyhedra in a dipole, a pentagram and a generic graph. We find that vector geometries, structures with neighboring polyhedra having adjacent faces glued back-to-back, arise from Bell-network states. We also discuss the relation to Regge geometries. The results presented show clearly the role that entanglement plays in the gluing of neighboring quantum regions of space.