Thermal bound entanglement in macroscopic systems and area laws

TL;DR

This paper demonstrates the existence of bound-entangled thermal states in harmonic oscillator systems, revealing that global entanglement can be undistillable locally within certain temperature ranges, linked to entanglement-area laws.

Contribution

It provides explicit calculations showing bound entanglement in thermal states of many-body systems and connects this to entanglement-area laws, extending to spin chains.

Findings

Bound-entangled thermal states exist in harmonic oscillator systems.

No distillable entanglement in certain temperature ranges.

Results suggest a link between entanglement-area laws and bound entanglement.

Abstract

Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By explicit calculations of the negativity for different partitions, we find a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We offer an interpretation of this result in terms of entanglement-area laws, typical of these systems. Finally, we discuss generalizations of this result to other systems, including spin chains.