Distinction of Tripartite Greenberger-Horne-Zeilinger and W States Entangled in Time (or Energy) and Space

TL;DR

This paper explores and distinguishes two classes of three-photon entangled states in space and time, revealing their similarities to GHZ and W states through correlation function analysis.

Contribution

It introduces a novel analysis of tripartite entangled states in continuous variables, highlighting their behavior and distinction in space-time configurations.

Findings

Three-mode state resembles W state behavior.

Two-mode triphoton state resembles GHZ state behavior.

Correlation functions effectively distinguish the two classes.

Abstract

In tripartite discrete systems, two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. To date, much research effort has been concentrated on the polarization entangled three-photon GHZ and W states. Most studies of continuous variable multiparticle entanglement have been focused on Gaussian states. In this Brief Report, we examine two classes of three-photon entangled states in space and time. One class is a three-mode three-photon entangled state and the other is a two-mode triphoton state. These states show behavior similar to the GHZ and W states when one of the photons is not detected. The three-mode entangled state resembles a W state, while a two-mode three-photon state resembles a GHZ state when one of the photons is traced away. We characterize the distinction between these two states by comparing the second-order correlation functions $G^{(2)}$ with the third-order correlation function $G^{(3)}$.