Distillable entanglement and area laws in spin and harmonic-oscillator systems

TL;DR

This paper investigates bound entanglement in many-body spin and harmonic oscillator systems, showing its persistence at finite temperatures and linking it to area laws, with analytical and numerical evidence across various models.

Contribution

It provides the first explicit calculation of thermal bound entanglement in harmonic and spin chains, establishing its intrinsic nature and connection to entanglement-area laws.

Findings

Bound entanglement exists at finite temperatures in harmonic and spin chains.

Thermal bound entanglement persists for arbitrarily large harmonic systems.

Bound entanglement is an intrinsic feature linked to area laws in these systems.

Abstract

We address the presence of non-distillable (bound) entanglement in natural many-body systems. In particular, we consider standard harmonic and spin-1/2 chains, at thermal equilibrium and characterized by few interaction parameters. The existence of bound entanglement is addressed by calculating explicitly the negativity of entanglement for different partitions. This allows to individuate a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We discuss how the appearance of bound entanglement can be linked to entanglement-area laws, typical of these systems. Various types of interactions and topologies are explored, showing that the presence of bound entanglement is an intrinsic feature of these systems. In the harmonic case, we analytically prove that thermal bound entanglement persists for systems composed by an arbitrary number of particles. Our results strongly suggest the existence of bound entangled states in the macroscopic limit also for spin-1/2 systems.