# Entanglement and non-locality of four-qubits connected hypergraph states

Copyright (C) 2020 Grâce Amouzou, Jeoffrey Boffelli, Hamza Jaffali, Kossi Atchonouglo and Frédéric Holweck.

Contact: gamouzou[at]univ-lome.tg

## Description

We study entanglement and non-locality of connected four-qubit hypergraph states. One obtains the SLOCC classification from the known LU-orbits. We then consider Mermin’s polynomials and show that all four-qubit hypergaph states exhibit non-local behavior. Finally, we implement some of the corresponding inequalities on the IBM Quantum Experience. For a given hypergraph state, we calculate its maximum violation of Mermin’s inequalities by optimization process. We then construct the hypergraphstate on the IBM Quantum Experience and make the measurements to verify the theoretical results. Maple was also used to determine the orbit or SLOCC families of four-qubits hypergraph states. It is based on the evaluation of invariant and covariant polynomials. Two algorithms were implemented : the first one determines the Verstraete family of a given state, and the second one determines the corresponding strata of the nullcone for nilpotent element. A third type of algorithms is proposed to determine the singular type of a hyperplane section which is a SLOCC invariant of the corresponding state.

Two softwares where used for this study: Maple and the python library Qiskit. The code used on those softwares are distributed in their respective folders: in the Maple folder and in the Qiskit folder.

A more literal description of the code can be found in the article [ABJ+20].

## Copyright

This program is distributed under the GNU GPL 3. See the enclosed file LICENSE.

## References

[ABJ+20] Grâce Amouzou, Jeoffrey Boffelli, Hamza Jaffali, Kossi
Atchonouglo, Frédéric Holweck. **Entanglement and Non-Locality of Four-Qubit
Connected Hypergraph States** arXiv:2010.03217