Quantifying Tripartite Spatial and Energy-Time Entanglement in Nonlinear Optics

TL;DR

This paper introduces a method to quantify genuine tripartite entanglement in continuous-variable states using the Tripartite Entanglement of formation, demonstrating its effectiveness in photon triplets from nonlinear optics.

Contribution

It develops a new measure for tripartite entanglement applicable to pure and mixed states and predicts its effectiveness in photon triplet systems generated by nonlinear optics.

Findings

The measure quantifies genuine tripartite entanglement in continuous-variable states.

Ordinary nonlinear optics can generate substantial tripartite entanglement.

The method is effective for photon triplets from cascaded SPDC.

Abstract

In this work, we provide a means to quantify genuine tripartite entanglement in arbitrary (pure and mixed) continuous-variable states as measured by the Tripartite Entanglement of formation -- a resource-based measure quantifying genuine multi-partite entanglement in units of elementary Greenberger-Horne-Zeilinger (GHZ) states called gebits. Furthermore, we predict its effectiveness in quantifying the tripartite spatial and energy-time entanglement in photon triplets generated in cascaded spontaneous parametric down-conversion (SPDC), and find that ordinary nonlinear optics can be a substantial resource of tripartite entanglement.