Tripartite and bipartite entanglement in continuous-variable tripartite systems

TL;DR

This paper analyzes tripartite and bipartite entanglement in Gaussian continuous-variable systems, revealing conditions for entanglement and the limitations of analogies to GHZ or W states, highlighting the versatility of tripartite quantum systems.

Contribution

It provides analytic solutions for entanglement properties in symmetric and asymmetric Gaussian systems and explores their relation to known entangled states like GHZ, W, and T states.

Findings

Symmetric systems show perfect tripartite correlations only at infinite squeezing.

Realistic squeezing parameters yield both bipartite and tripartite entanglement.

Systems produce T states but are not fully analogous to GHZ or W states.

Abstract

We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and bipartite entanglement. We conclude that none of the outputs are completely analogous to either GHZ or W states, but there are parameter regions where they produce T states introduced by Adesso \etal The qualitative differences in the output states for different interaction parameters indicate that continuous-variable tripartite quantum information systems offer a versatility not found in bipartite systems.