# Proposed optical realisation of a two photon, four-qubit entangled $\chi$ state

## TL;DR

This paper proposes an optical method using hyper-entangled photon pairs to efficiently generate four-qubit $ ext{chi}$ states, which are useful for quantum information processing.

## Contribution

It introduces a simple quantum circuit and optical setup for preparing $ ext{chi}$ states using hyper-entangled photons from SPDC.

## Key findings

- Successful generation of $ ext{chi}$ states via optical setup
- Use of hyper-entanglement in polarization and OAM
- Simple transformations produce different $ ext{chi}$ states

## Abstract

The four-qubit states $\lvert\chi^{ij}\rangle$, exhibiting genuinely multi-partite entanglement have been shown to have many interesting properties and have been suggested for novel applications in quantum information processing. In this work we propose a simple quantum circuit and its corresponding optical embodiment with which to prepare photon pairs in the $\lvert\chi^{ij}\rangle$ states. Our approach uses hyper-entangled photon pairs, produced by the type-I spontaneous parametric down-conversion (SPDC) process in two contiguous nonlinear crystals, together with a set of simple linear-optical transformations. Our photon pairs are maximally hyper-entangled in both their polarisation and orbital angular momentum (OAM). After one of these daughter photons passes through our optical setup, we obtain photon pairs in the hyper-entangled state $\lvert\chi^{00}\rangle$, and the $\lvert\chi^{ij}\rangle$ states can be achieved by further simple transformations.