graphepp 0.3

A collection of functions for multipartite entanglement purification protocols (EPP) on noisy graph states

GraphEPP

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

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]