Macroscopic bound entanglement in thermal graph states

TL;DR

This paper demonstrates the existence of bound entanglement in thermal graph states of large spin systems, showing that entanglement can be present without being extractable through local operations at certain temperatures.

Contribution

It proves thermal bound entanglement exists in large spin systems with finite-range interactions, using bipartition independence of entanglement.

Findings

Bound entanglement persists at certain temperatures.

Entanglement cannot be extracted via local operations.

Examples provided for 1D and 2D systems.

Abstract

We address the presence of bound entanglement in strongly-interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one- and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.