Entanglement in macroscopic systems

TL;DR

This paper develops criteria and measures for detecting entanglement in large, macroscopic quantum systems, analyzing how entanglement persists or decays with system size and temperature.

Contribution

It introduces multipartite entanglement criteria and an operational measure for systems with fluctuating particle numbers, with analytical examples involving harmonic oscillators.

Findings

Entanglement detection becomes more challenging as system size increases.

Detectable entanglement decays with macroscopic particle numbers without decoherence.

Thermal states show temperature-dependent entanglement behavior.

Abstract

We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems with a fluctuating particle number. To access the quality of the verified entanglement, the operational measure of the entanglement visibility is introduced. As an example, we perform an analytical characterization of quantum systems composed of interacting harmonic oscillators and witness the entanglement via energy measurements. Our analysis shows that the detectable entanglement decays for macroscopic particle numbers without the need for decoherence processes and for all considered coupling regimes. We further study thermal states of the given correlated system together with the temperature dependence of entanglement.