GraphEPP

GraphEPP is a collection of functions for multipartite entanglement purification protocols (EPP) on noisy graph states.

Installation

You can install GraphEEP into your python environment from the Python Package Index: (possibly overwriting already installed package versions in your environment with its dependencies):

pip install graphepp

As with all python packages, this can possible overwrite already installed package versions with its dependencies, which is why we recommend installing it in a dedicated virtual environment.

If you encounter any problems, you can try installing it the exact versions of GraphEPP's dependencies that were used to develop it (specified in Pipfile.lock). This assumes Python 3.8 and pipenv are installed on your system:

git clone https://github.com/jwallnoefer/graphepp.git
cd graphepp
git checkout main
pipenv sync
pipenv install graphepp

and then use pipenv shell to activate the virtual environment

Scope

This project provides functions for operations on quantum states that are diagonal in the graph state basis corresponding to a chosen graph state. (for an introduction to graph states see e.g. arXiv:quant-ph/0602096) These include:

• Local Pauli-diagonal noise channels that are applied on qubits of the graph state.
• Distance measures for states given in the same graph state basis.
• The ADB protocol for two-colorable graph states introduced in Phys. Rev. Lett. 91, 107903 (2003) and Phys. Rev. A 71, 012319 (2005).
• The protocol for all graph states introduced in Phys. Rev. A 74, 052316 (2006).

as well as auxiliary functions like local complementation of graphs.

Example use case: Perform multiple rounds of EPP on a noisy linear cluster state of 5 qubits when the CNOT operations used in the EPP are themselves imperfect (e.g. modeled by local depolarizing noise).

Publications

An earlier (unreleased) version of GraphEPP was used for these publications:

Two-dimensional quantum repeaters
J. Wallnöfer, M. Zwerger, C. Muschik, N. Sangouard, and W. Dür
Phys. Rev. A 94, 052307 (2016)
Preprint: arXiv:1604.05352 [quant-ph]

Measurement-based quantum communication with resource states generated by entanglement purification
J. Wallnöfer and W. Dür
Phys. Rev. A 95, 012303 (2017)
Preprint: arXiv:1609.05754 [quant-ph]