Extracting GHZ states from linear cluster states

Abstract

Quantum information processing architectures typically only allow for nearest-neighbour entanglement creation. In many cases, this prevents the direct generation of GHZ states, which are commonly used for many communication and computation tasks. Here, we show how to obtain GHZ states between nodes in a network that are connected in a straight line, naturally allowing them to initially share linear cluster states. We prove a strict upper bound of $\lfloor (n+3)/2\rfloor$ on the size of the set of nodes sharing a GHZ state that can be obtained from a linear cluster state of $n$ qubits, using local Clifford unitaries, local Pauli measurements, and classical communication. Furthermore, we completely characterize all selections of nodes below this threshold that can share a GHZ state obtained within this setting. Finally, we demonstrate these transformations on the IBMQ Montreal quantum device for linear cluster states of up to $n=19$ qubits.

6 pages, 4 figures, Jupyter notebook available at https://github.com/hahnfrederik/Extracting-maximal-entanglement-from-linear-cluster-states

References in corpus (7)

• Multi-party entanglement in graph states
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Quantum Anonymous Transmissions
• Secure Anonymous Conferencing in Quantum Networks
• Limitations of nearest-neighbour quantum networks
• Fidelity measurement of a multiqubit cluster state with minimal effort
• Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration

Cited by in corpus (8)

• Flexible quantum data bus for quantum networks
• Hardware-Efficient Preparation of Graph States on Near-Term Quantum Computers
• Transforming graph states via Bell state measurements
• Graph state extraction from two-dimensional cluster states
• The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
• Distinguishing Graph States by the Properties of Their Marginals
• Localizing multipartite entanglement with local and global measurements
• Polynomial-time Extraction of Entanglement Resources