Extracting GHZ states from linear cluster states

TL;DR

This paper presents a method to generate GHZ states from linear cluster states in quantum networks, establishing bounds, characterizing possible node sets, and demonstrating the approach on a real quantum device.

Contribution

It introduces a new protocol for converting linear cluster states into GHZ states, with theoretical bounds and experimental validation.

Findings

Established a strict upper bound of  (n+3)/2 for GHZ state size from linear clusters.

Characterized all node sets below the bound that can share GHZ states.

Demonstrated the transformation on IBMQ Montreal with up to 19 qubits.

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.