Complete analysis of the maximally hyperentangled state via the weak cross-Kerr nonlinearity

TL;DR

This paper introduces a practical method for fully analyzing maximally hyperentangled states across multiple photons and degrees of freedom using weak cross-Kerr nonlinearity, enhancing quantum communication capabilities.

Contribution

The proposed method enables complete hyperentangled state analysis for two, three, and N-photon systems using weak cross-Kerr nonlinearity, combining nonlinear interaction with linear optics.

Findings

Effective analysis of two-photon hyperentangled Bell states.

Complete three-photon hyperentangled GHZ state analysis.

Feasible with current technology for high-capacity quantum communication.

Abstract

We present a simple method for the complete analysis of maximally hyperentangled state in polarization and spatial-mode degrees of freedom assisted by the weak cross-Kerr nonlinearity. Our method not only can be used for two-photon hyperentangled Bell state analysis and three-photon hyperentangled Greenberger-Horne-Zeilinger (GHZ) state analysis, but also is suitable for N-photon hyperentangled GHZ state analysis. In our protocols, the bit information of hyperentanglement is read out via the nonlinear interaction, and the phase information is obtained by using linear optical element and single photon detector. This approach is achievable with the current technology, and will be useful for the practical high-capacity quantum communication schemes.