# Quantum hyperentanglement and its applications in quantum information processing

**Authors:** Fu-Guo Deng, Bao-Cang Ren, Xi-Han Li  
**arXiv:** [1610.09896](https://arxiv.org/abs/1610.09896)  
**Date:** 2016-10-31  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1610.09896v1/

## Key points

- Hyperentanglement refers to entanglement in multiple degrees of freedom (DOFs) of a quantum system
- Hyperentanglement allows for the utilization of various DOFs such as polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs of photons
- Progress made in the field of hyperentanglement in photon systems is reviewed
- Important applications of hyperentanglement in quantum information processing are discussed
- Advancements achieved include hyperentanglement generation, complete hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification for high-capacity long-distance quantum communication
- A scheme for a hyper-controlled-not gate is introduced, enabling simultaneous controlled-not gate operations on both polarization and spatial-mode DOFs with minimized resource consumption and photonic dissipation
- The review highlights the potential applications of hyperentanglement in advancing quantum information processing

## Summary

Hyperentanglement, which refers to the entanglement in multiple degrees of freedom (DOFs) of a quantum system, has emerged as a promising resource in quantum information processing. This high-capacity characteristic of hyperentanglement allows for the utilization of various DOFs such as polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs of photons to carry information. In this review article titled "Quantum hyperentanglement and its applications in quantum information processing," authors Fu-Guo Deng, Bao-Cang Ren, and Xi-Han Li provide an overview of the progress made in the field of hyperentanglement in photon systems. They also discuss several important applications of hyperentanglement in quantum information processing. The authors highlight key advancements achieved so far, including hyperentanglement generation, complete hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification for high-capacity long-distance quantum communication. These developments have paved the way for enhanced capabilities in quantum information processing by utilizing all available DOFs fully. Additionally, the review introduces a scheme for a hyper-controlled-not gate that enables hyperparallel photonic quantum computation. This scheme allows for two controlled-not gate operations on both the polarization and spatial-mode DOFs simultaneously while minimizing resource consumption and photonic dissipation. Overall, this comprehensive review provides valuable insights into the field of hyperentanglement in photon systems and highlights its potential applications in advancing quantum information processing. The findings presented here contribute to ongoing research efforts aimed at harnessing the power of hyperentangled states for future advancements in quantum technologies.