# Environment mediated multipartite and multidimensional entanglement

## TL;DR

This paper explores how an engineered environment can facilitate the formation of multipartite and multidimensional entanglement in quantum systems, challenging the notion that the environment always destroys entanglement.

## Contribution

It demonstrates that a reservoir can mediate entanglement among qubits and qudits at low temperatures and intermediate coupling, with a new witness for multipartite entanglement.

## Key findings

- Multipartite entanglement can form via environment mediation.
- Entanglement witness based on structure factor is effective.
- Possible experimental measurement of entanglement proposed.

## Abstract

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.