# Preparing Greenberger-Horne-Zeilinger and $W$ states on a long-range Ising spin model by global controls

## TL;DR

This paper develops methods to prepare GHZ and W entangled states on a long-range Ising spin model using global controls, providing analytical solutions for GHZ and a scalable approach for W states.

## Contribution

It introduces analytical solutions for GHZ state preparation and a scalable numerical method for W states in long-range Ising models using global controls.

## Key findings

- Analytical solutions for GHZ state preparation for any system size.
- A standard, scalable method for W state preparation demonstrated numerically.
- Number of parameters increases linearly with system size.

## Abstract

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and $W$ states are two inequivalent classes of multipartite entangled states which can not be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and $W$ states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the $W$ state, we find a standard way to prepare the $W$ state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.