Thermal state entanglement in harmonic lattices

TL;DR

This paper explores how thermal states in harmonic lattices exhibit entanglement, identifying critical temperatures for entanglement between neighboring sites and discussing boundary effects and methods to manipulate entanglement.

Contribution

It determines the critical temperature for entanglement in harmonic lattices and introduces techniques for swapping and tuning entanglement experimentally.

Findings

Critical temperature for entanglement between neighboring sites identified

Boundary effects influence entanglement in larger systems

Proposed methods to swap and tune entanglement experimentally

Abstract

We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites are shown to be entangled only due to boundary effects. Other forms of entanglement are addressed in the second part of the paper by using the energy as witness of entanglement. We close with a comprehensive diagram showing the different phases of entanglement versus complete separability and propose techniques to swap and tune entanglement experimentally.